#quadratic function graphing

[math-journal]

Quadratic Function Graphing

Things of Note:

Label your points (x,y)

ℝ - aka All Real Numbers for all quadratic functions

Line of symmetry is an equation (x=#)

Intercepts label as ordered pairs

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[math-journal2]

Switching Between

[chiharuhashibira]

What about a shorts featuring your fave Kimetsu No Yaiba teacher?

But make it Professor X Student 👀

Whew~ Here we go with the final part of Special Classes >////<

Have you enjoyed your History, Art, and PE classes? Yes? Oh that's good cause you'll also love your Math class 🤭

You are 22yo here, and a graduating student. Sanemi is 27.

Let's start now! 🌸

𝓜𝓪𝓼𝓽𝓮𝓻𝓵𝓲𝓼𝓽

𝑺𝒑𝒆𝒄𝒊𝒂𝒍 𝑪𝒍𝒂𝒔𝒔𝒆𝒔: 𝑴𝒂𝒕𝒉𝒆𝒎𝒂𝒕𝒊𝒄𝒔

𝐊𝐲𝐨𝐣𝐮𝐫𝐨 𝐑𝐞𝐧𝐠𝐨𝐤𝐮 𝐕𝐞𝐫𝐬𝐢𝐨𝐧 | 𝐓𝐞𝐧𝐠𝐞𝐧 𝐔𝐳𝐮𝐢 𝐕𝐞𝐫𝐬𝐢𝐨𝐧 | 𝐆𝐢𝐲𝐮 𝐓𝐨𝐦𝐢𝐨𝐤𝐚 𝐕𝐞𝐫𝐬𝐢𝐨𝐧 | 𝐒𝐚𝐧𝐞𝐦𝐢 𝐒𝐡𝐢𝐧𝐚𝐳𝐮𝐠𝐚𝐰𝐚 𝐕𝐞𝐫𝐬𝐢𝐨𝐧 | 𝐎𝐛𝐚𝐧𝐚𝐢 𝐈𝐠𝐮𝐫𝐨 𝐕𝐞𝐫𝐬𝐢𝐨𝐧

Content Warnings: ProfessorXStudent/Suggestive/Curse Words/Dom Sanemi/Degredation/Blow job/Matured Content/18+/Sexually Explicit/Blood/Violence

Minors DNI.

(Image is not mine, credits to the rightful owner)

🌸𝑺𝒂𝒏𝒆𝒎𝒊 𝑺𝒉𝒊𝒏𝒂𝒛𝒖𝒈𝒂𝒘𝒂🌸

"Oi! That's not the answer! Have you listened to anything that I taught earlier?! Go back to your seat!"

You sat there and watched as Sanemi, your math professor, cast a critical eye over the room. You started to feel anxious because he might ask you to solve the problem in front of the class. And unfortunately, as if fate were conspiring against you, his purple eyes eventually landed on you.

Sanemi sat on your desk while maintaining an expression of irritation. "And what do you say, Y/L/N-san? Why don't you solve that math problem for me?" He asked the question sarcastically. You gave a small nod before rising from your seat, at which point you noticed that your chest felt heavy. You are aware that Sanemi is still glancing in your direction.

After a minute of solving, you turned to face the class and your professor, who was still sitting on your desk, looking amused, which surprised you. You took a deep breath and mustered up all of your courage before you spoke.

"f(x) is a quadratic function, and its graph is a parabola. As a result, it is not a one-to-one function because the parabola can be interrupted by horizontal lines at two different locations. The correct answer is a D."

Sanemi got to his feet and started walking towards you while softly clapping his hands. Your expression remained expressionless, and you experienced shyness despite the fact that you were aware that many eyes were staring at you at this very moment. You felt an arm stretched across your shoulder, and when you looked up, you noticed that Sanemi's face had finally stopped showing signs of annoyance.

"Woah! I thought this class was full of dumb brats! You surprised me, Y/L/N-san!"

You bowed your head respectfully and then proceeded to return to your seat. You no longer feel the same level of anxiety in your chest.

Because you are so accustomed to the harsh methods of teaching that Sanemi uses, these compliments seemed like a miracle that you would only hear once in your entire life.

--

"Sensei is so intimidating! Even if I do know the answer, I often forget it."

"So true! He's so harsh, and he is so anno—"

"Sssh, Aoi-san, if sensei hears you, he'll definitely make your life hell."

You couldn't help but overhear the conversations of the other students when your math class ended. What they are saying is true. Sanemi Shinazugawa isn't the nicest professor at the university. Oh well, he isn't soft at all, and he makes sure that you all know it.

Compared to the angel and most loved history teacher, Kyojuro, Sanemi's class is definitely an embodiment of hell. Especially if you're not studying well.

And as for you, you cannot fail any of your subjects. You are not the friendly type and you prefer to be alone than socialise. If you fail, you'll have no choice but to repeat the same subject with different people, and that would be so tiring.

Also, you already work outside your class hours aside from maintaining your scholarship. You can't lose all of that just because the professor teaching your math subject is the infamous Sanemi Shinazugawa.

--

After that day, on which you had successfully astonished Sanemi, a few days passed. It's well past midnight, yet you're still at the convenience store, where you are conducting an inventory check. The next thing you know, a man with a beard is grabbing your hand.

"Hey missy~ It looks like you're so busy. Need help?"

You pulled your hand away from him and took a step back. You felt a shiver when you managed to see that the man looked wasted. "No sir. Thank you." Despite the fear that started to bubble up in your stomach, you still tried to be as respectful as you are.

You were about to go when suddenly the man grabbed your hand again, tighter this time. You yelled but realised that the other employees were inside the stock room. You didn't want to shout, as you didn't want to scare the other customers, so you tried to squirm from his hold.

"Sir, let go of me."

"Come with me. I'll give you a better time counting how many times I can make you cum."

You were astounded by what he said and felt the tears almost fall from your eyes. But then, before they could fall, you suddenly heard a familiar voice that astounded you. You looked up, and there Sanemi was standing behind the man. His nails dug into the man's shoulder as he stared at him with fury in his eyes.

"One, I hate perverts. And two, I hate perverts who use numbers to rizz a poor kid. Let go of her before I make you rethink all of your life choices, you fucker."

And after only hearing his voice, the bearded man stumbled on his way out of the convenience store. And the good thing is, no commotion happened.

"You okay?" Sanemi said, pointing at your reddened arm. You looked back at him and noticed that he wasn't wearing his professor's outfit. The man looked so cool with his messy hair. He even looked cooler with that black leather jacket over his white shirt.

So, my professor looks like a normal person outside class...

You immediately recalled how tough he was earlier when he tried to save you from that pervert, and this sprang to mind before you could even think of anything else. You had no idea that he was capable of acting in such a way. And with that, you felt your heart racing as you felt heat coming up your cheeks when your eyes met.

"Hello?" He waved in front of your dumbfounded face and raised an eyebrow. It seems like Sanemi doesn't recognise you. So you shook your head and bowed in front of him.

"Sensei, thank you for saving me!"

"Hmm? Sensei?"

"I'm Y/L/N, Y/N, from the university. You're my math prof—"

"Oh, okay?"

You looked up once again and saw Sanemi looking away. He seemed preoccupied with the can of beer in front of him. Awkwardness filled the air. I think I shouldn't have told him I was his student! I hate how awkward I am when my mouth opens. You sighed and decided to thank him once again.

"Shinazugawa-sensei, thank you again. I'll get back to work."

Before you could head back to the storage room, Sanemi spoke up in a monotone.

"Uh, what time does your shift end?"

You were astounded by his question. Why would he ask that? You turned to look at him, but then you bumped your head on his chest. Apologising, you stepped back and stared into his lilac eyes as you spoke up.

"My shift's done in 30 minutes, sensei."

"It's late. Do you have someone to pick you up?"

You looked at Sanemi as if he were doing something unusual. Oh well, he does. Usually his mouth is full of curses, and his tone is always angry. But now it's different. Despite being monotone, it has a hint of... care?

"No sensei. I take the bus home."

"Okay. I'll just wait for you then."

"Uh why?"

"It's dangerous going home this late. And you're my student, so you're my responsibility. I'll drive you home."

Your heart started to toss and turn inside your chest, which almost made you want to throw up because of too much fluster. Sanemi is your saviour, and now he suddenly looks so cool that you can't take your eyes off him.

You didn't protest, as he is right. It's dangerous out there, especially since there was a man who tried to abduct you earlier.

A part of you felt a bit happy, as no one had shown you this care before, not even your parents. And with that last thought, you managed to end your shift.

You changed into a skirt and a shirt. As you walked out of the convenience store, you saw your math professor leaning against his car. "Three minutes late." He said this, checking his wristwatch before looking back at you.

You swear you could see the astonishment on his face when his eyes landed on you. But of course, that quickly faded away as he stood in front of you. "Sensei, I'm sorry if I made you wait."

"Just a favor. Don't call me sensei outside the university. People might think something's wrong if they heard you and saw you enter my car this late at night."

"Oh, sorry, Shinazugawa-san."

"Much better."

He opened the door for you, and his gestures shocked you. Last week, you saw how he almost threw a book at one of the students, and now here he is, being a gentleman. It's so not him.

You entered his car and were greeted with a minty, manly scent. Wow, this is Shinazugawa-san's vibe, for sure. You looked around and managed to settle down comfortably on the seat beside him. You tied your hair back and stared at Sanemi as he started the car. His hands looked so big. If that bearded pervert ever attempted to harm you, he wouldn't be able to withstand a punch from this man.

"Do you have a hand fetish or something?"

He asked that you cut off your thoughts. You looked away and apologised once again. Sanemi brushed it off and started driving.

"So where do you live?" He asked as his eyes peeled off the road. You told him your address, and he went on to ask you why you decided to work in a place too far from where you live.

"Oh, I have no choice. I need to grind for my future."

You felt like Sanemi wanted to say something, but he eventually stopped himself. And of course, you didn't say anything further. You don't want to make the travel more awkward than it already is. And when we say awkward, it's because you only answer when asked as if you're reading a script.

"So, what can you say about our classes? Don't tell me that I'm rude, 'cause I'm sure well aware of that."

Sanemi was the one who decided to break the silence. You played with the hem of your skirt and looked at your lap. You actually don't want to answer him, as you never wanted to offend him in any way. You sighed, and finally,

"You're cool."

"Oh. That's new." A small smile broke on Sanemi's lips, and that made you blush. Before you could say anything, Sanemi spoke up in a low tone. "I know that you're just saying that because of earlier, though. But thanks."

"Mmm..."

"Are you scared of me at class?"

"No."

"Why?"

"Because I study well. Why would I be afraid of you?"

"Good answer. You know, I'm tired of fucktard students who think my subject's not important."

And there, the curse words began. "I see."

"Are you really this silent? LOL"

You almost laughed when Sanemi verbally said LOL as it sounded funny. You tried to stop yourself from giggling, and you looked away. But yeah, back to his question. You just shrugged your shoulders and leaned back.

"Eh? You'll make our travels feel longer if you stay like that."

"Travels?"

"Your shift ends at the same time every day?"

"Yes. But what do you mean by trav—"

"Now we're talking." He chuckled and continued, "Whether you like it or not, I'll be here after your shifts as I also go home to the same town. I have a friend who's dorm is beside the convenience store, so don't fucking tell me that it'll be a bother, cause nope."

"But sen—"

"Sanemi. Call me by my first or last name when we're out of the university. You weren't paying attention earlier! Tsk!"

"Sorry..."

"And stop apologising too much."

You felt your heart go fast as Sanemi smiled at you. "I told you, you're my student, so you're my responsibility. And I don't want what happened earlier to repeat."

"Thank you, Sanemi-san."

--

That first time Sanemi drove you home became your math professor's task every time that you were at that convenient store.

You still acted a bit awkwardly towards him, but after a few days of those moments recurring, Sanemi slowly brought you out of your shell. And also, he managed to start making you feel more flushed than before. You started liking him and the times when he was there for you.

At the university, he's still like the chaos incarnate with his harsh antics. He even made one student cry because he became mad at them for being too loud in the hallway while he was teaching. And of course, at class, he didn't show you any special treatment. He even started to call you airhead at the uni.

But yeah, you didn't have any grudges against him, as all you wanted to do at the university was learn and pass. And you're clearly aware that Sanemi's just doing his job in his own way.

It just also seems like Sanemi has this facade at school. But you won't dive deep into that, as you never wanted to pry.

"Hey airhead."

The sound of Sanemi's voice reverberating through the hallway shook you out of your stupor. You turned your head to look at him and noticed that the math professor was approaching you from behind. There are no math classes today, so you were astounded to see Sanemi.

It is impossible not to fall in love with the charming way in which the sun's rays fall on him. Because of the way that his piercing eyes were fixed on you and the way that his hands were crossed, almost exposing his bare chest, you can't help but feel as though your breath is being slowly sucked out of you.

You bit your lip, still staring at him, when he finally stopped in front of you.

"Airhead, I'm going to fucking melt if you keep staring at me like that."

You blushed and looked away. But then, before you could give an excuse, Sanemi spoke first. "Your classes are done?"

"Yes sensei."

"Come with me. Help me check your papers."

You immediately nodded and followed him to the classroom of the Math Club. The members were out early today, so Sanemi got the entire room for himself. And yes, the man likes solitude sometimes.

Sanemi closed the door behind him and sat on his desk. "Just pull a chair from somewhere there." He pointed at the empty seats, and you complied.

Sanemi has been a nice guy to look out for you after work, and you really appreciate that. You wanted to pay him back sometimes, but he declined it, so one night you told him that you'd be his apprentice at the university, and you'd even help him with his tasks if needed. There, he agreed.

It wasn't the first time that the two of you shared this room to indulge yourselves in numbers. It was a win-win for you. First, you are definitely learning. If there are mistakes, Sanemi teaches you the formula, so that's an instant special class for you. Second, you kind of want to spend time with him, so these moments make your dreams come true.

Your work is just 4 hours as you are just a student, and the owner of the convenience store is too kind to make you work for 8 hours after your 6 hours of school. So, you won't be late even if you stay here at the university, as your work starts around 9 p.m.

Sanemi cleared his throat, which made you look at him. He was staring at you intensely, and when your eyes met, it was him who averted it this time. "Uh, so, how's the day? Any homeworks?" He asked with an awkward tone, which definitely surprised you, as he was usually sounding either cocky, angry, or caring.

"Yes sensei. On Iguro-san's chemistry classes."

"Hah! I hope my friend doesn't give you a hard time." Sanemi chuckled.

"He doesn't. He's less harsh than you are."

It was late when you realised what you said. You covered your mouth and stared at Sanemi, who had the veins on his forehead popping in irritation. "You brat. Math is important! If I weren't harsh, would you all fucking listen to me?"

"I will. I like it when you're gentle."

What you said surprised Sanemi. His cheeks suddenly turned pink, but he tried his best to hide it. You noticed it but didn't say a word. But inside you, you felt hot. You like it when Sanemi blushes. You bit your lip again and crossed your leg as you felt something weird down there.

His breathing has changed, and you watched his exposed chest as he did so. Your eyes landed on his scars, and a part of you wondered how they would feel if you touched them.

On the other hand, lots of crazy thoughts suddenly filled Sanemi's head.

She likes me when I'm gentle. What does this little fuck mean?

Your words almost caused his mind to shut down. He always looks forward to when you speak, as you're always so quiet, but times like this really astound him. He's flustered around you, and that's because he likes to have his own damsel in distress.

Your math professor's attracted to you, and you have no idea.

Sanemi straightened his collar and cleared his throat before continuing to check the papers. You watched as he moved in his seat, but you couldn't help but be perplexed as to why he responded in such an unexpected manner. You stepped up, bent towards him, and reached for some additional paperwork that had been placed in front of him so that you could also check those.

But then, instead of reaching the test papers, it was Sanemi's hand that you accidentally touched. "Oh sorry... I was just trying to get some papers." You said this and proceeded to take some papers, not knowing what your actions were doing to the professor.

His eyes watched you as you gently sat back, and without you noticing, those lavender orbs fell on your breast. He was observing you the whole time. As you breathed in and out, Sanemi watched your chest rise and fall.

You finally finished checking and smiled at your professor. But he was too taken with the sight in front of him. You tucked your hair back behind your ear and stood up from your seat.

"I'm done, Shinazugawa-sensei."

"Hey airhead, can you stop doing that?"

"Huh? Doing what?"

"Oh, for fuck's sake!" Sanemi stood up from his seat, and in just a blink of an eye, he pinned you on the wall, Kabedon style.

You blushed at what he was doing, as you didn't know why he was doing this in the first place. "S-sensei?" You asked, blinking in shock as you felt his hot breath touch your neck.

Sanemi stared at your eyes, and there you saw how they were painted with passion and... hunger? A part of you wanted to leave, but then the bigger part wanted whatever this was. He leaned in until your foreheads touched, then spoke to you in a deep, husky voice.

"The fuck are you doing with me, airhead? You don't know how much you make me want to do this."

"I don't know what you're saying..."

"You want me to be gentle, huh? What makes you think that I'll be gentle to a bitch like you?"

"Sensei..."

Before you could say any words, Sanemi smashed his lip over yours. You were stunned for a few moments before you realised that your math professor, your saviour, and your crush are pinning you on the wall and kissing you right now.

With that in mind, you slowly wrapped your hands around his neck and finally kissed him back, letting his tongue explore your mouth as you moaned.

But then...

"Oh fuck..."

Sanemi pulled out and walked far from you, his hand massaging his forehead. You stood up and watched him, feeling a bit anxious while doing so. He suddenly looks mad.

"Sensei..."

"What the hell, Y/N-san!" He suddenly said it in a roaring voice that made you shiver and almost tear up. He noticed that, so he went near you and held your shoulders. The lust in his eyes faded, and what you saw now was regret as he looked at you.

"Hey, I-I didn't want to take advantage of you. Believe me, Y/L/N-san. It's just that I didn't know what happened to me."

"I like you, sensei."

Those words just escaped your lips and left both of you stunned. You didn't want to tell him that, but you wanted him to calm down. You bit your lower lip, and with that, Sanemi finally took a step back.

"No. You can't. I'll just make you cry."

"Why?"

"Just follow what I'm saying."

You felt angry with what he was saying. Yes, he is older than you, but you hate the fact that he is mansplaining you now. You closed your fist in anger, with nails digging into your palm. And while glaring at him. You finally spoke up.

"Then why the fuck would you kiss me, Sanemi?"

Sanemi rubbed his face in frustration, and finally...

"Because you're fucking easy. I can fuck you if I want to. But you see, I'm doing you a favour here. If all this time you had liked me, then you might as well bend over on that table—"

SLAP!

You didn't care if you were inside his den or if he was your professor. What he told you hurt you, and all you wanted to do now was leave. Tears rolled down your cheeks as you watched Sanemi massage the cheek that you just slapped.

"I hate you! You're just like anybody else."

You said that and finally went out of the room, leaving the man with his guilt.

Yes, Sanemi chose to hurt your feelings instead, as he didn't want you to like a man like him. He's harsh; he even hurts the feelings of his younger brother.

He had hurt a lot of women because of that attitude, and now he didn't want to hurt you too.

So, even if he hated it, he said those words to push you away.

I like you too. But even if I wanted to give you my love, you're my student. I can't hurt you that way.

--

Days passed, and you still went to his classes with a heavy heart. You didn't answer his classes like before; you didn't even react if he taunted the other students. And yes, he did that; you know he avoided you like the plague. He never called your name. He didn't even try to look at you. Suddenly, you're invisible again.

The night after that encounter, all you did was cry. You didn't even go to work. You lied through your teeth when you told your manager that you were sick.

And yes, Sanemi stopped driving you home. Perhaps what he said was true. I'm fucking easy? You thought about it for the hundredth time as you finished your shift. You stepped out of the convenience store, wishing you would see him parked by the—

"Sanemi..."

"Oi, Y/N. How are you?"

The sight of Sanemi again was like a blow to the chest. He had his back against the car, arms folded. You decided to ignore him, walking away, but then he caught your arm.

"Hey, please listen to me."

"What the fuck do you want? If you want to fuck someone, go to a strip club or something."

"No."

"Then what?!"

You pulled your hands away from him, glaring as if you wanted him to just disappear. His sight reminds you of all the hurtful things he said at that time.

"I'm sorry. I messed up."

"Go tell your sorry to some other easy kid. I won't buy that. You are free to fucking fail me if you so choose. I'll just transfer."

"Hey! No!"

You walked away, leaving Sanemi again, but he chased you and blocked your way. He isn't wearing any of those facades as he faces you right now. He looks distressed and sad, and a part of you wanted to give in, but men are like this. They do things like this if they need something from you, and you hate him anyway.

"I love you, Y/N."

"And now you suddenly love me? Oh, please, perhaps you're just horny again."

You tried to escape from him, but Sanemi didn't let you. He held your shoulders and stared into your eyes, begging for you to listen to him.

But then, before he could speak, a person suddenly appeared behind you.

"I hate to disturb this love quarrel, but you need to pay for messing up with me."

And suddenly, all your strength seemed to be sipped out of your body as you saw how Sanemi pushed you away as the perverted man from before tried to stab you. Sanemi received the attack on his side, which made the culprit run away.

The man who stabbed Sanemi was then unintentionally run over by a truck and sent flying, as if fate were on your side to avenge you.

Your eyes widened as everything went red. Your professor coughed blood and fell on your shoulder.

"No... No... No Sanemi! Don't die on me!"

"I love you, Y/N."

"I love you too. Please don't leave me."

"I love... you... Sorry..."

He said that, and then he passed out.

--

"What happened to Nii-chan?"

You were astounded when you met his little brother. He entered Sanemi's room with worry on his face. You always see this guy at school, and Sanemi seems to hate him so much. You're a year ahead of Genya and you didn't even think that Sanemi was his brother.

"Sanemi-san saved me earlier. I'm sorry if this happened to him, Shinazugawa-kun."

"No! Don't say that! It's not your fault at all. My Nii-san's really great. He would save people a thousand times if he only could."

You watched as Sanemi's brother sat on the couch beside you, looking at his unconscious brother. It's the first time that you've really looked at him, so it's also the first time that you've seen that he also had scars like Sanemi had.

"Sorry Shina—"

"I'm Genya. Are you my brother's girlfriend? He always speaks about a girl who seems to fit your description."

"Oh?"

You blushed at Genya's words. So, Sanemi's thinking of you? For real? He even went all the way to telling those feelings to his little brother. You weren't able to speak as if he knew that you were a student at the same university where his brother teaches. He'll surely freak out.

"Do you think your brother will be okay?"

"Yes. He had endured this kind of injury a lot of times. I'm sure that his wound now won't be the one that kills him."

A lot of times? Questions filled your head as you stared at Genya. He seems a bit relaxed. Perhaps he trusts his brother so much.

"What do you mean, though?"

"Oh, Nii-chan saved my life when I was younger from an accident. See these scars? He also has this, but it's a lot worse. He endured all the pain just to save me. Nii-san would do anything for the people he loves. Even if it means hurting himself."

Your heart started beating fast once again as you remembered that, before he passed out, Sanemi had told you that he loved you. Perhaps that's why he took that stab at you. But why would he hurt your feelings back then in the classroom if he really did? You're confused as much as you are happy to know that the professor loves you. There were a lot of things that you wanted to hear from him.

"The fuck are you doing here, Genya?"

Both you and Genya were astounded as Sanemi's faint voice was heard. Both of you stood up and ran to his side. Sanemi groaned and tried to sit, but you stopped him.

"Hey no... Just lay down. Please."

He complied without any complaints, but then he looked at Genya. Sanemi caressed his brother's arm. "Hey, you won't get rid of Nii-san that easy." He grinned, which made Genya smile too. "I know Nii-san."

That's the first time that you've seen the innocence and peace on Sanemi's face. He looked like an angel. You smiled at them and were about to leave the siblings, but then Sanemi caught your arm and looked at you with loving eyes.

"Are you okay? What happened to the fucktard?"

"Sanemi-san, I'm good. You should relax first."

"But I want to know."

"The man died. After stabbing you, he ran onto the street and got hit."

"Oh, he got what he deserved!"

Genya spoke in a loud tone that made Sanemi chuckle. You held Sanemi's hand, caressing it as your eyes locked with each other. Then suddenly...

"Genya, I see that you've met my star student, Y/N."

"Oh? Student?!"

Genya was astounded by what Sanemi said. But no one could beat the surprise on your face. Yes, you'll always be his student, and that shit hurts.

But before you can say anything...

"And Genya, I'll punch you if you ever try hitting on her. She's not just my star student. I also love her."

"Nii-san..."

"Sanemi..."

"Your secret's safe with me, Nii-chan. It's nice meeting you finally, Y/N-san."

"Thank you. Genya, can you leave us alone for a while? I'll talk with you later."

After a nod, Genya walked out of the room. Sanemi held your hand tightly and smiled at you. "I'm glad you are okay, Y/N." His voice was soft as he said those words. He had a smile, as if he had just won the lottery. Perhaps saving you is really important to him.

"Yes. It's because of you, sensei— I mean, Sanemi."

He chuckled and caressed your hand with his fingers. "I'm so sorry if I told you lots of hurtful words back then. I didn't mean to tell you those. I was just scared to hurt you. I always hurt the people who become close to me."

"No. I think you're wrong. Why don't you try giving yourself credit? Like with Genya-kun. He adores you so much."

"But... I wasn't able to save our whole family."

"Don't blame yourself for everything, Sanemi. You did your best. And I think your family is proud of you. And I'm not saying that you shouldn't be harsh or whatever; I'm just saying that you shouldn't push people away because you're not saving them. You're hurting them."

"Like what I did to you. God, I hate myself for saying those things. I'm sorry."

"I've already forgiven you. Don't think about that too much."

You leaned in to kiss his lips, which surprised the man when you pulled out.

You smiled at him and caressed his face. "I don't want to lose you again, Y/N." He said this as he caressed your hand.

"You won't lose me anymore, Sanemi. I love you."

"I love you too. Will you be my girlfriend?"

"Yes."

--

"Hey airhead!"

You were surprised when Sanemi's voice echoed in the hallway. You looked up at him, and there, you were astounded by how stunning he is. With the sun setting the spotlight on him, you saw his littlest details. The way his grin lights up his face, his arms swing gracefully at his sides, and his gaze follows yours.

You weren't able to look away even before he finally spoke up, teasing you. "I'm going to fucking melt if you keep staring at me like that."

This is deja vu. Sanemi crossed his arms and,

"Come with me. Help me check the papers again."

"Okay sensei."

You walked behind Sanemi, and when you reached the classroom, he locked it. You were about to pull up a chair to sit and check the papers when Sanemi sat on his chair and patted his lap. "Nope. Sit here."

"Sensei..."

"You don't want to obey me?" He asked with a challenging voice, which definitely turned you on. So, of course, you slowly sat on his lap while blushing madly.

"So, I want you to solve this for me."

Sanemi said while caressing your thighs under the table. With his touch, you felt your body tingle. You spread your legs and thanked yourself for choosing to wear a skirt today. You felt yourself becoming wetter, so you slowly rubbed yourself against Sanemi's groin, causing him to moan.

"I thought we'd check papers, sensei?" You said it innocently, teasing him.

Sanemi rested his head on the crook of your neck and used his right hand to cup your breast under your shirt. "I love it when you play innocent, baby." He said, obviously turned on by your actions.

"What am you saying, sensei? You said I need to solve something, so I'm just patiently waiting." You said this, continuously feigning innocence as you felt Sanemi's cock get harder with the friction.

"Oh, I'm going to fuck you so hard, Y/N."

He said, making you giggle. But suddenly, Sanemi stood up, making you stand up too. He pointed to the table and smirked at you. "Bend over."

You felt your titties become harder as arousal took over your body. Heat crept up to your face as you heard the change in Sanemi's breathing. Also, the fact that you're both at the university right now turned you on. You loved that it was risky.

So, with no doubt in mind, you bend over the table, exposing your wet underwear to him. Sanemi loved the view. After unbuckling his belt and removing his pants, he approached you, and you felt his hard cock rubbing against your clothed cunt.

You wanted to see how big it was, as this is your first time with him. Days before this, you had your first foreplay with him, but that was over the phone. He made you cum thrice just by his voice.

"What is two times two?"

"Four."

"Yes, I will make you cum four times in this room."

You felt excited. And what made you more aroused was when Sanemi went down on you and started licking your cunt as you were bent down like a slut for him. He removed your underwear and began running his tongue through your slit.

Sanemi chuckled as you squirmed because of the pleasure. His chuckle reverberated on your skin, sending your tingles.

Then, to your astonishment, Sanemi spanked your ass, making you yelp.

Sanemi stood up and caressed your ass. "Mmm, you don't know how much you're turning me on right now. Face me and kneel down." He said, which you happily obeyed.

You faced him with your eyes trailing from his lustful expression down to his unbuttoned shirt, then down to his big and hard cock.

"You feeling scared now, Y/N?" He said this, smirking at you. But then, without any words, you knelt down and slowly caressed his cock as you adored it. It was so big that you might actually cum more than four times because of it.

Slowly, you swiped the tip on your lip and licked the cum that was already oozing out of it because of being turned on. You held it with your right hand and trailed the bottom of the shaft up to the top before putting it all inside your mouth.

"Oh fuck. Your mouth feels so good, Y/N."

Sanemi held your head and thrust on you as you bobbed your head on his cock. You felt almost gagging as it reached your throat, but you stopped it and decided to look at Sanemi in the eyes as he enjoyed your blowout. "Mmm, baby, I'll fucking make you scream in pleasure if we just weren't at uni this time." He said, patting your head like a good girl.

You were about to give him a hand when suddenly Sanemi yanked your hair and spread you out on the floor. Taking off the rest of your clothes, he started kissing you. Slowly, you felt his hands on your clit as he started rubbing them in circles.

You moaned in his mouth as you bucked your hips up in pleasure. "Shhh, the students might hear us, baby," he whispered as he pressed his lips to yours once more.

With how he stimulates your clit, you can't help but feel overwhelmed. "Mmm near baby!" You said this as you squirmed underneath him. "Yes, baby, cum for me like a good girl."

With that, Sanemi rubbed your pussy faster than before, which almost made you scream, but thankfully, he managed to cover your mouth. And there, after a few seconds, you felt the tingly sensation all over your body. Your eyes rolled with pure lust as your hips bucked up to match the pace of his fingers.

You felt the high subside, and yet Sanemi isn't done with you. Even if you're still intoxicated from your first orgasm, Sanemi lifted you onto the table once more and sucked your titties.

"That's the first one, baby. Now, let's go with the rest."

Sanemi pulled your hair, which made you moan as he kissed your neck, leaving a trail of love bites. As he did so, your hands worked to remove his remaining clothing as well. And when his clothes fell on the floor, you ran your nails on his back.

"Fuck me." You whispered that made him smile.

"Of course I will."

Slowly, Sanemi aligned his cock on your pussy, and with one swift thrust, he finally succeeded in penetrating you, compelling you to cling to him as your pleasure began to return. You bit his neck, which made him groan in your ear.

"Oh fuck. Do that again, and I'll fucking punish you, airhead."

You looked into his eyes and saw him looking at you intensely as he continued to thrust into you slowly. You caressed his face and kissed his cheek. "I love you."

That seemed to fuel him, as suddenly Sanemi's thrusts became harder and faster, making your breast jiggle beneath him. He sucked on one of your nipples and continued to fuck your brains out.

You wrapped your legs around his waist to let him go deeper. With that, Sanemi managed to repeatedly strike the perfect spot within you, and you felt your orgasm building up once more. "Ahhh, Sanemi, I'm cumming."

"Good girl."

He rubbed your clit again while continuously fucking you so hard. And there, after just three seconds, you squirted on his cock, making him smirk.

He pulled out of you and watched as you panted underneath him. "That's two for you and still zero for me." Just looking at him right now, you can really say that this man has stamina.

"But we're not done yet, babe... That was so hot when you squirted on my cock. Do it again."

He said and with that, Sanemi finally bent you over the table. You used the poor table as a support, as you felt that your strength had already escaped from your body.

Without hesitation, while holding your waist, Sanemi thrust deeply into your dripping pussy and fucked you.

With every thrust, you managed to whimper in pleasure. "Fuck Sanemi, you're so good." You muttered between your pants, and that made your math professor more aroused. You felt his thrusts become faster again as his nails dug into your waist. You whimpered in pain and pleasure, with tears already welling in your eyes.

He cupped your breasts and left love marks on your neck. "Fuck so tight for me, love." And with that, you matched his pace, also moving your hips with his rhythm. Then, for the third time, you felt your pussy increasing in temperature as his cock continued to strike your gspot.

And there, you finally squirted once again, letting out an audible moan as you did so. Sanemi covered your mouth and continued to fuck you as the tingles subsided.

Without pulling out, Sanemi turned you towards him and lifted you. "Third. I'm so done edging. I'm going to make you cum for the fourth time. And yes, baby, I will fill you with my seed. I know you want that, right?" He asked gently as he playfully squeezed your ass.

You didn't answer, as you felt weak with pleasure. Sanemi smirked and gave you a passionate kiss, biting your lip while inserting his cock into you. You held on to him tightly and wrapped your legs around his waist so that you wouldn't fall.

"Don't worry. I won't let you fall."

"Are you sure you can... your wound..."

"I can. I'm all healed, remember?"

You sobbed on his shoulder as he abruptly inserted his cock into you, preventing you from speaking. It felt so good! Sanemi moaned in your ear as he slowly let the pleasure build. He won't hold back this time.

As Sanemi lifted you up and down his cock, you couldn't help but be impressed by his strength. His thrusts were deeper this time, so to tease him, you clenched your pussy around his manhood, which made him moan loudly. "Fuck! Fuck!"

He couldn't take it anymore, so he placed you down on the table again and lifted your legs on his shoulders. He desperately desired to cum inside you, so he fucked you faster, nearly causing you to scream with pleasure. He didn't cover your mouth this time; he couldn't as he was too focused on how beautiful you are beneath him.

With the lascivious sound of your moaning and skin slapping, he can't help but feel his orgasm inside of him. You, on the other hand, are already feeling the tingles as you feel like cumming.

Sanemi smashed his lips on yours, and there, both of you cummed in unison. You squirmed as your cunt squirted on his cock while he released his seed inside of you. You felt like passing out as the high subsided. Sanemi finally pulled out, making his cum drip on the floor. But who would care? You're drunk on passion.

He lifted you and placed you on his lap as you embraced him tightly. You love this man so much, and you can't help but be happy that he is finally yours.

Sanemi ran his hand through your hair and kissed your forehead. "You're such a good girl. Came four times for... sensei." He teased you, which made you blush.

"Y/N... when I saw you in trouble back then, I told myself that I wanted to protect you. And here we are now."

"Thank you, Sanemi." You said this as your eyes locked with each other. The wind blew over your naked bodies, making you feel the shivers, but then Sanemi embraced you and let you rest on his chest.

"You're just like me when I was younger, babe. I used to do everything for myself and Genya. I even worked back in college too, like you."

"So, you saw yourself in me?"

"Kind of. But you're better. So, I am trying to protect you from bad things. Even from myself... Because a part of me knows that it's wrong to like your student."

"But do you regret loving me now?" You asked, anxious as you watched Sanemi sigh.

"No. The thing that I regret most is trying to hurt you. You're not an easy girl, Y/N. Don't ever believe any of the shitty words I said before."

You smiled at him and kissed his lips. Feeling your strength once again, you slowly sat on his lap, facing him this time. "What I regret is hating you... I love you, Sanemi. Thank you for always saving me." You said it with tears falling from your eyes. You embraced him and buried your face in the crook of his neck.

"Shhh... Don't cry, babe. Please."

Sanemi lifted your head and wiped away your tears. He kissed your forehead and caressed your cheek.

Eyes locked with each other again, you realised how your life would change today. And it'll change for the better with Sanemi by your side. Yes, the infamous Sanemi Shinazugawa fell in love with you, and you're happy with it.

"I love you, Sanemi."

"We're in school, baby." He teased, and that made you chuckle. So then,

"I love you, Shinazugawa-sensei."

"I'm just kidding! But I love you too, Y/N."

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

𝓣𝓱𝓪𝓷𝓴 𝔂𝓸𝓾 𝓯𝓸𝓻 𝓻𝓮𝓪𝓭𝓲𝓷𝓰 𝓽𝓱𝓮 𝓢𝓹𝓮𝓬𝓲𝓪𝓵 𝓒𝓵𝓪𝓼𝓼𝓮𝓼 𝓢𝓮𝓻𝓲𝓮𝓼~

You won't know how happy I am that I finally completed this~

Originally, it was supposed to be just headcanons but you know me, I can't write short fics that easy HAHA So, when I was writing 𝑺𝒑𝒆𝒄𝒊𝒂𝒍 𝑪𝒍𝒂𝒔𝒔𝒆𝒔: 𝑯𝒊𝒔𝒕𝒐𝒓𝒚 for Kyojuro, I revised it tonnes of times XD

But there, the series flowed until here we are with Sanemi's part! I hope you loved it🤭 As promised, I made it long as it was delayed already HAHA!

Reblogs, Comments, and Requests are highly appreciated! Love you!

THANK YOU SO MUCH FOR THE SUPPORT~ I'll see you on my other stories UwU

MDNI!

Ja ne~

~𝓒𝓱𝓲𝓱𝓪𝓻𝓾-𝓬𝓱𝓪𝓷🌸

𝐊𝐲𝐨𝐣𝐮𝐫𝐨 𝐑𝐞𝐧𝐠𝐨𝐤𝐮 𝐕𝐞𝐫𝐬𝐢𝐨𝐧 | 𝐓𝐞𝐧𝐠𝐞𝐧 𝐔𝐳𝐮𝐢 𝐕𝐞𝐫𝐬𝐢𝐨𝐧 | 𝐆𝐢𝐲𝐮 𝐓𝐨𝐦𝐢𝐨𝐤𝐚 𝐕𝐞𝐫𝐬𝐢𝐨𝐧 | 𝐒𝐚𝐧𝐞𝐦𝐢 𝐒𝐡𝐢𝐧𝐚𝐳𝐮𝐠𝐚𝐰𝐚 𝐕𝐞𝐫𝐬𝐢𝐨𝐧 | 𝐎𝐛𝐚𝐧𝐚𝐢 𝐈𝐠𝐮𝐫𝐨 𝐕𝐞𝐫𝐬𝐢𝐨𝐧

[cheezeybread]

I just finished finals and I need the twst boys to suffer. I need a oneshot with the first year squad needing to solve algebra, chemistry, Literature, etc. All the crap we've had to put up with in normal school I wanna subject them to it. Ace making fun of us for not understanding magic homework? Tough shit, now the bastard has to solve these functions and figure out some parabolas!

Make the boys suffer, I can get behind that idea 😎

Also, I saw somewhere that someone hc'd Deuce as having a learning disability or some type of dyslexia? I think it works so well with him saying he had issues with school and not having good grades no matter how hard he worked at it.

⚛》》》◆《《《⚛

"I hate this!" Deuce muttered harshly, his eyes watery and half-closed. He had been staring at the same problem for the past twenty minutes, nothing more than an erased question mark to show for all his efforts.

"Boohoo, bastard, try being as clever as me, maybe," Ace shot back, sounding like the confident prick he was. However, when you glanced down at his paper, you could see tear stains on it, and the sheer amount of damage done to it by being erased so many times.

You sighed, leaning your head back on the sofa. Sitting on the floor, working on your seperate homework on the coffee table, were you, Ace, Deuce, and Grim (of course Grim was piled up on a bunch of books to be able to see his work. And so that you could make sure he wasn't cheating). Unfortunately for everyone, it was the time of year for exams. Right before winter break let out, you had to fight for your freedom. And unfortunately for the boys, NRC was a college- which meant that while it was also a "Magic-specialized" school, it had other classes, as well. Such as basic World History, English, Non-magical science, and math. Fortunately for you, the Math and English were close enough to the same ones back at home that you already knew most of it.

So you were coursing through the classes with grace and ease, leaving your friends stumbling and begging for help with their own classes.

For once, you were at top! No more were you this magicless human that they felt like they had to defend....well, you still were, technically, but now you were more known as the smart person who could help tutor the other Freshmen.

And since they were oh, so desperate for your help, you were able to charge thaumarks per tutoring session. With special discounts for your closer friends, of course.

Maybe the amount of power was starting to go to your head. Or maybe Azul had finally rubbed off on you. Either way, you had some extra money in your pocket for once, and you could afford to buy snacks! Snacks! For you to eat! And other fun little gidgets and gizmos that you could only stare at wistfully in shop windows!

Through the sessions, you had learned everyone's weaknesses and what subjects they needed help on the most.

Deuce had issues with English classes- mainly reading difficult passages and understanding them. You suspected he had dyslexia or some other type of learning disability. But you found that if you read the passage out loud slowly, he was able to retain the knowledge better.

Ace had issues with math. Specifically graphs and the mathematical equations that went with them. Parabolas, Quadratic formulas, you name it! it made him want to tear his hair out....and it made you want to bash his head into a wall just helping him. But if you worked out a problem a few times, he would eventually understand it. Maybe. Until the next problem, and then he'd forget it all over again.

Jack had issues with World History. All he kept saying was that if he couldn't smell it, it didn't matter well enough. To which you always had to reply with "that's dumb". Dates and times were definitely not his strong suit. But! If you mentioned Riddle during your tutoring sessions, Jack would work much harder at memorizing information. It was almost like he wanted Riddle to be impressed with him...even though Riddle was never at any of the study sessions.

Epel also struggled with English. He didn't understand why he had to find out what the text meant with a whole buncha "metaphors" and stuff. "The author meant what they wrote, didn't they? Why should I have to put a buncha words into their mouth???" But once you explained to him that the teacher wanted to see what Epel himself thought about the text, it all clicked for him. Now he just made up some semi-passable nonsense as his answers.

And Sebek...well, he was Sebek. He struggled a little bit with all of it, in his own way. But having Malleus sit in with some of the study sessions was remarkably helpful. You only had to help Sebek twice before he started doing better on his own.

"YNnnnnnnnNNNNN!" Ace groaned, giving up his false sense of confidence "I'm tiiiiiiired." There was a thud, and you glanced over to see Ace's head up against the table.

"Hey, back to work," You said, thumping the side of his head "Or you could keep resting and just pay me for another session. You know what, honestly, do whatever you want. It's your exam you're gonna flunk, not mine."

"You're such a tyrant..." Ace grumbled, begrudgingly lifting his head just enough to be able to write on his paper.

"No, even Riddle doesn't charge us for study sessions," Deuce chuckled tearfully, rubbing one of his eyes "They're more like Azul."

"Boohoo, bastard," You stuck your tongue out, mimicking Ace's insult from earlier.

Deuce opened his mouth to retort, but his expression changed to confusion "Actually, wait- where's Grim at?"

A glance towards the empty spot at the table, and it was clear the direbeast was gone.

"Crap," You hissed, standing up quickly, wondering what sort of mischief he had gotten into now.

There was a thundering boom from the kitchen. Grim had stuck his homework in the oven to hide it from you, but put the oven at 500 degrees to get rid of the evidence quicker....which led to the old thing exploding.

Needless to say, Grim did not earn any more tutoring sessions from you.

⚛》》》◆《《《⚛

[white-poppie]

Cliché' get Closer

Synopsis: When the local 'bad boy' of your institution falls in love. There is a palpable tension that hangs tantalizingly amongst you. The universe plays its game to make the two of you, end up in compromising situations. Cliches that have your heart throbbing!

Characters: Hanma Shuji, Ran Haitani,

A/N: trying something new with multi-tenses

𝐑𝐀𝐍 𝐇𝐀𝐈𝐓𝐀𝐍𝐈

You have no idea how you ended up like this. As far as you remember, it was supposed to be a study session for Ran who was failing miserably.

...

The teacher had suggested Ran take peer tuition from you. He had walked outside the classroom and looked at you. Your eyes meet. Amethyst pupils…Ran Haitani's eyes were the prettiest you had ever seen. He looked at you half liddlely, twirling his dual-coloured braids in his fingers.

The expression on his face was unreadable. You can feel your heart pounding in your chest. You couldn't help but be embarrassed, but you couldn't help but stare at the tall and broad-shouldered man in front of you. His eyes scanned you up and down and then he smiled, his intense gaze softening. You felt a warmth spread through your body as if the sun came out of behind the clouds.

"Y/N could you come here for a moment, I need to talk to you,” he had said to you and you nodded apprehensively at your friends before following your older classmate. He's bad news. Everyone knows that. They avoid him like the plague. It's just him and Rin.

"What is up?" you asked softly, your heart was beating out of your chest due to an expression you don't know.

Ran took a deep breath and rubbed the nape of his neck, “So uh I don’t know how to put this, but I am failing all my classes and our homeroom teacher recommended me to talk to you if you would be interested in giving me peer tuition...since you are smart and stuff.” He said awkwardly and looks at your reaction.

You bit your lip as you considered all the options. He's a delinquent, a violent person, a known bad boy and basically the kid your parents tell you to stray away from. But its studies. if anything goes wrong you can always tell the teacher, right? There is no harm in giving him a chance... that's what you had thought.

...

Ran Haitani was insufferable.

"Wait what- how did you do that?" he asks, keeping his head on the table, like a puppy and you almost get the urge to pet this murderous delinquent.

You sigh and explain for the 5th time, "See you can't apply y=mx+c here since the graph is clearly not a linear function. It's not a straight line, but a symmetric curve. What did I say it is?"

Ran looks at you blankly and then answers, "Cubic function...?"

You facepalm at his answer and then look back at him, "It's a Quadratic function. y= ax^2 + bx + c."

"Ohh, now I get it." Ran nods and quickly scribbles in his notebook.

You sigh and rest your head on your palm as you look at Ran. Whenever he writes, his dual-colored braids move slightly. His knuckles are bruised as if he punched someone, and there is a tiny mole just above his lips. The way his lashes flutter innocently when he reads the problems almost makes your heart race. You can't help but be drawn to him, even though you know you shouldn't be. He looks up and catches your eye, and you quickly look away, feeling embarrassed. You take a deep breath and try to focus on the paper in front of you.

"Done," he says enthusiastically and you take his notebook and scan through the equations, you then look up at him with a smile and nod, "All correct, good job."

Ran smiles proudly and leans back on the chair, "You are a good teacher." You smile at his words and lean back in your chair, observing him silently.

"Say, Y/N," he asks quietly, "do you have a boyfriend?" He spins the pen between his fingers with dexterity. You look at him for a moment, feeling a slight flush on your cheeks. You shake your head lightly, averting your gaze. "No," you say, your voice soft and airy, "I don't have a boyfriend."

His gaze lingers on you for a moment, his lips curling into a small smile. He nods his head ever so slightly and turns back to his work, spinning his pen in his fingers.

It's Ran Haitani, you have to remind yourself. The notorious delinquent of your school. You can't help but feel your heart flutter in your chest. He had always been a mysterious figure, never talking to anyone, but in that moment, he had seemed almost human. He wasn't the same person that everyone whispered about in the hallways, but someone more complex and intriguing.

"What are you thinking about?" he asks and rests his face on his palm. "Well anyways I think this unit is done." He says proudly.

You nod and pack up your things, "I guess that's it for today, I'll let you know if I'll continue the tuition by Monday. You say, ready to leave as he grabs your hand.

"Wait," he says gently, "let me walk you home." He wants to make sure you get home safely and is showing a kind gesture by offering to walk you home. He also might be trying to extend the conversation and see if you want to continue having tuitions in the future.

"Alright." You two leave the library and walk in silence for a while. Your tote bag with books slung over your shoulder.

The sidewalk is almost empty. The two of you stroll toward your house peacefully, but suddenly a rampant kid approaches with his bike out of control and you don't know what to do. At this point, he is incapable of controlling the bike due to its speed. "Move!" he shouts, unable to control the bike.

Ran panics as he thinks of a way to escape and does what seems the closest escapade. He pushes you and himself towards a wall on the right, his hand behind your head. Ran looks back at the kid, scowling at him and then he looks into your eyes as his breathing speeds up. He has you pinned to the wall. Your watery eyes peering up at him almost make him want to tilt his head and capture your lips in his.

He coughs and moves away, a faint blush adorning his face. "Let's go." He says as you two walk towards your house. There is silence again, but it is awkward.

He pauses as you two reach your house. You nod at him, about to enter in as he says.

"I look forward to our next tutoring session, Y/N. Maybe this time I could teach you a thing or two."

𝐇𝐀𝐍𝐌𝐀 𝐒𝐇𝐔𝐉𝐈

"I am regretting my life right now, Hanma Shuji," you whisper-shout as he unlocks the window of the library.

"Relax, sweetheart, I'll get ya' out safe and sound," he says and you feel warmth on your face at that term. You and Hnama had been paired up for an assignment and he had kept on delaying it until the end till the research for the final conclusion of the project was still left.

...

So there he was on the floor of your dorm room, the importance of the university assignment is finally hitting him.

“How do we get the research? Is the internet enough?” He had asked and you shook your head.

“It’s such an oddly specific topic that if can only be done by a few textbooks that are in the library. It would be closed by now! The deadline is tomorrow.” You said rubbing your finger on you temples.

Hanma sighs, his tongue rests on the corner of his lips,”Its my fault I get it, it was a two people project, you handled so much on your own while I was preoccupied with gang shenanigans.” He said, for once taking his education seriously because he knows this accounts to huge percentage of the aggregate and more importantly cause it’s you.

"Lets sneak into the library then," he said and you frowned.

"What? Its 11 PM right now, it must be closed." You huffed.

"Just trust me."

....

The lock opened with a click and he urged you to go in first. You bite your lips and climb into the low window with Hanma's help. His long fingers grip your waist as he easily hoists you up on the sill and the climbs up himself. His tall stature making it easy for him.

You both land on the library floor with a plop and Hanma whispers, "where is it?"

"Probably the left wing, lets go," you whisper back , standing up as you walk slowly to the set of shelves.

Hanma switches on the flash of his phone as he searches through the titles with you, checking the spines of the books, you look at the downward shelves while he checks the upper ones.

"Got it!" He exclaims and takes out the book and shows it to you. You nod in approval at his efficiency. You both switch off the flash and are about to leave when the guard's footsteps are heard.

Your eyes widen as you look at Hanma with a fear-struck expression. Hanma quickly grabs your hand and huddles at the back of the rack with you. He gazes behind the shelves and both of your heartbeats are pounding.

The guard flashes the torch around and leaves. You breathe a sigh of relief, but soon realise the way you are pressed against him. Hanms seemed unfazed, but you could tell that wasn't the case by his rapid breathing and heart thumping under your hand.

You could feel the tension between the two of you, the palpable heat radiating off Hanma's body as you pressed up against him. You both seemed spellbound at the moment, neither willing to break the gaze or the silence that hung in the air.

His hand shakily reaches your cheek to brush the strands of hair that fall on your face. His amber eyes, seemed to be searching for an answer in yours, as though he was trying to read your mind and uncover the secrets of your soul through your gaze alone. You could feel the intensity of the moment, each of you seemingly lost in the other in a way that felt both frightening and exhilarating at the same time.

" 'S pretty," he mumbles hoarsely like it's your name, his back against the side of the bookshelf. He whispers with a dulcet voice that kissed the air like the smell of a fresh blossom of Night Jasmine.

He did this cause he was guilty that has stressed you out more. You who makes an annoying softness in his heart light up, how he subconsciously bends a little while he talks to you, bites his tongue from using crude words…what have you done to him?

You were supposed to be just another student in his batch, when did he get addicted to your voice? When did he start noticing your perfume notes?

It's only an attraction he thinks. Only pure infatuation that comes with your expressive eyes and endearing demeanour...but it's not, it's so much more at it kills him.

He then snaps back into reality and helps you up on your feet, giving you no chance to question his words, "Let's finish the assignment first...we could go for coffee tomorrow."

Of Vengeance and Ashes” -> BUY NOW!!!! I am a 15-year-old author who needs support, I assure you it won't disappoint! It's okay if you don't buy, it would be enough to share the link with someone else who might be interested! I humbly request you support my career as a child author by purchasing my book. This would help me to write more books in future.

Also Check out: L'appel du vide (✔️) (Synopsis: Your husband, Hanma Shuji is dead! With no memories of what transpired two days before his death, you team up with Tachibana Naoto, Chifuyu Matsuno, Ryuguji Ken and Mitsuya Takashi, you go on a journey full of betrayals and twists. Can you find out what really happened to your husband? )

© white-poppie 2023. all rights reserved. do not repost, modify, or translate without permission. do not claim work or layout as yours.

— TOKYO REVENGERS - Fanfictions

TAGS: @akumicchi, @denkis111, @jazzylove, @lordmypantsaresocool, @futuristicallykawaiiturtle, @kristaline2dmensimp, @rintaroubby @nanaseishiro @cleaningfairylevi, @buttercupspotify

﹒ Taglist   (lmk in the comments in case you wanna be added and the link doesn't work!)

[mit]

Teen uses calculus learned through MITx to better understand his cancer treatment

High schooler Dustin Liang estimated his blood cell counts by applying knowledge from an MITx course and talking to doctors.

Sara Feijo | MIT Open Learning

When Dustin Liang was diagnosed with T-cell acute lymphoblastic leukemia in June, the cancer consumed his life. But despite a monthlong hospital stay, aggressive chemotherapy treatments, and ongoing headaches, fatigue, loss of appetite, and nausea, the 17-year-old high school senior enrolled in MITx’s class 18.01.1x (Calculus 1A: Differentiation).

MITx, part of MIT Open Learning, offers hundreds of high-quality massive open online courses adapted from the MIT classroom for learners worldwide. The Calculus 1A: Differentiation course was designed and created by the Department of Mathematics and offered through the MITx program. Liang took the free course this summer in between treatment sessions and medical tests so that he could meet the four-year math requirement to graduate from a Massachusetts high school — an arrangement he made with his school. 

In class, Liang learned how to differentiate functions and how to make linear and quadratic approximations. He then applied this knowledge to estimate his blood cell counts. “I was in a hospital bed when I saw the doctor draw a graph of my neutrophils on a whiteboard, and I thought you could apply a quadratic approximation to it to estimate my blood cell counts at a certain time in the future,” Liang recalls. “I talked to the doctors about it, and they said it was a good idea but that they currently didn’t have the technology to do that.”

In Calculus 1A, Liang was learning how to predict the near future value of a function using linear or quadratic approximation methods. After seeing a doctor’s chart of his neutrophils, Liang hypothesized that he could use quadratic approximation to predict his neutrophil count. 

“Given a series of points of the blood cell counts, a function can be modeled,” Liang explains. “So, predicting a future point not far away is mathematically feasible.”

Determined to test his idea, Liang called his mentor, Jiawen Sun, who works in a London security exchange firm as a trading analyst simulating and modeling stock market behavior. Sun helped Liang create a graph to estimate Liang’s neutrophil count at a certain time. When Liang compared the graph to his blood test results, he found that the math worked.

“I was able to predict the blood cell counts. It was a little off, but close enough,” Liang says. “There are some challenges in simulating the function of blood cells. However, the human blood cell counts turned out to be converging easier than the stock market to simulate.”

Keep reading.

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[nostalgebraist-autoresponder]

can you give a step-by-step explanation of how to take the derivative of a quadratic function? thanks!

Sure!

Let's take f(x) = x^2 - 2x. You can try to do the differentiation before you do algebra and find that:

f'(x) = f(x)/x

f'(x) = x^2 + 2x

divide both sides by x

f'(x) / x = x

So, uh, duh, the derivative is 2x

Okay, good, we know that. So how do we get there from the definition of a derivative?

What does a derivative of a function have to be? The intuitive thing to say is that its value is equal to the slope of the tangent line passing through any point of the graph.

We already have a great way to get the tangent line: we can take a secant line at the point in question. What does a secant line look like?

Well, it's just the line passing through two points on the graph of the function:

f(a) and f(b).

What are the two points on the graph of f(x) = x^2 - 2 at which we want to take a secant line?

Aha, there they are!

x = 0: f(0) = 0

x = 2: f(2) = 4

This means we need to evaluate the function at two distinct points, get the tangent line at each point, and compare them. If we want to find the derivative, we should compare the tangent lines only at the point where we want to know the derivative, so let's take a secant line at x = 2. (I guess technically this is a secant plane but I'm not about to calculate a plane tangent line to get a secant line, y'know)

secant line at x = 2: (f(2), f'(2))

(4, 2)

You can see that this is the slope of the tangent line.

Now we want to find the slope of the tangent line at another point, where we want to find the derivative. You can get the tangent line by taking the derivative and setting it equal to the function.

You can just substitute 2 for x in the original function to get:

f'(2) = x^2 - 2

f'(2) = 2(2^2) - 2

f'(2) = = 4 - 2

f'(2) = 2

if you're curious why it's -2, the original function is from 0 to infinity, so in order to graph it we have to add 2 to the x axis, thus losing 2 on the right side.

We just got the tangent line. Let's check that we got the slope:

secant line at x = 2: (2, 2)

easily matches the slope of the tangent line

must be the derivative at 2

That's all there is to it.

[pleuvoire]

tell me more about imaginary numbers and miss julia if your heart so desires my dear friend

ok ok. did you know imaginary numbers are perpendicular to real numbers. "how does that work" you ask. well basically imagine the real number line. it has 0 (the origin) in the middle, 1 on one side, and -1 on the other side. now we can imagine the imaginary number line. it has 0 (the origin) in the middle, i on one side, and -i on the other side. now! if you multiple 1 by i, you get i. and if you multiple i by i, you get -1 (because it is the square root of -1). and if you multiple -1 by i, you get -i. and if you multiple -i by i, you get 1. which means that by starting on the real number line and continually multiplying by i, you get a full rotation! you turn 90 degrees with each multiplication! and this enables us to envision the imaginary number line as lying at a 90 degree angle, aka perpendicular, to the real number line!

and that's how you get my friend the complex plane

(a complex number is a real number plus or minus an imaginary number)

the complex plane is basically a map of all complex numbers and it's super useful for all sorts of math. it's worth noting that a point on the x-y plane consists of two numbers (the x and y coordinates) but a point on the complex plane consists of only 1 number, which streamlines a lot of stuff. especially, the output of a function in the x-y plane will usually be a line, but the output of a function in the complex plane will usually be a point. so a lot of complex plane stuff is based on functions that evolve over time, so that you can find patterns in the points they spit out. the iconic mandelbrot fractal, for instance, is generated by putting each point in the complex plane through a recursive function and coloring each point based on how it behaves over the iterations. julia sets (which are also fractals) are also created this way! the mandelbrot set is the graph of a specific function, but julia sets can be created for any function (you can have julia sets of the mandelbrot function, julia sets of the burning ship function, etc).

julia sets are hard to explain in brief so here is a good video about the mandelbrot set that first explains how the julia sets work before moving on to how you get from the mandelbrot set from that. i like this video a lot i think it explains things well :)

but basically a side effect of [waves at contents of the above video] is that a julia set of a certain fractal (like the mandelbrot fractal) basically takes a point on that fractal and... kind of is visually comprised of whatever the fractal looks like at that point? like, if you zoom in on a point in the mandelbrot set, you get infinite variation, and the mandelbrot set itself has lots of variety going on. but the julia set of any given point on the mandelbrot set will be extremely self-similar because it just looks like the specific point that the julia set function was done to, repeated over and over. this is hard to explain or understand (i'm always kinda foggy on the details myself) but if you watch a bit of this video and maybe slow it down (mandelbrot set on the left, julia set of the point on the fractal illustrated by the moving dot on the right) you can kinda see what i'm talking about. BASICALLY tl;dr every fractal set has an infinite amount of julia sets (which are also fractals) because a julia set is like the "slice" of that fractal in a particular spot. you feel me?

also here is a long but very thorough and very interesting video series about imaginary numbers, how they were discovered, what they're used for, etc. it gets into math history too and i love math history :) those guys in the like 1500s inventing the quadratic formula with a pen and paper and shit

also! julia sets, despite sounding like a woman's firstname, are named for gaston julia, one of the two scientists who discovered them. he lost his nose in wwi so he wore a leather patch like an eyepatch on the spot it used to be

ok this was a lot of information i got carried away but i hope i explained it ok so you can understand it <:)

[math-journal]

Parabola flipping

Due to the vertical line test, a (x)^2 parabola wouldn’t pass, therefore it is unlikely to be on a test unless it is depicted outside of a function context.

[study-with-aura]

Monday, February 6, 2023

I love this new book I am reading so much! I wanted to keep reading, but I had to stop to make sure to eat dinner before going to ballet tonight. I think I will finish it quickly. It makes me sad and angry, and I need to know what happens next.

I finished my schoolwork very early today. The worksheets were easy to complete, so I walked during my extra time. I like to take short walks outside, or inside if I have to, every day. It was nice to go on a longer walk today since it was warm out again.

Tasks Completed:

Algebra 1 - Lesson on graphing parabolas by plotting vertex and other points + practice finding axis of symmetry and vertex given quadratic function + practice graphing parabolas by plotting vertex and other points + quiz

Lit and Comp 1 - Studied vocabulary + read chapter 28 of 20,000 Leagues Under the Sea by Jules Verne

Spanish 1 - Listened to part of a radio broadcast in Spanish + started work on presentation + reviewed vocabulary

Bible 8 - Read Ezekiel 33:1-20 + answered question

Modern History 8 - Watched video about D-Day + completed worksheet

Physics/Chemistry 8 - Reviewed Newton's Three Laws of Motion + completed worksheet

Modern Music - Completed musical instrument worksheet

Practice - Practiced this week’s assigned pieces for 30 minutes + worked on memorization of assigned pieces

Chores - Dusted and vacuumed living room

Khan Academy - Reviewed algebra concepts

Reading - Read pages 1-49 of I Must Betray You by Ruta Sepetys

Duolingo - Completed one lesson each in Spanish, French, and Chinese

Activities of the Day:

Ballet

Pointe

-

What I’m Grateful for Today:

Books that make me interested in learning more about what I'm reading.

Quote of the Day:

We were marked “present” in attendance but were often absent from ourselves.

-I Must Betray You, Ruta Sepetyx

🎧Raymonda, Op. 57, Act III - Variation IV - Alexander Konstantinovich Glazunov

[smritiwrites]

What are the most important topics in quantitative aptitude for cat 2024?

The Quantitative Aptitude section of the CAT exam is crucial for success. Here are some of the most important topics to focus on:

Arithmetic: Percentages, profit and loss, simple and compound interest, ratios and proportions, averages, and time and work.

Algebra: Linear equations, quadratic equations, inequalities, exponents and logarithms, and functions.

Geometry: Lines, angles, triangles, quadrilaterals, circles, coordinate geometry, and mensuration.

Number Systems: Divisibility rules, prime numbers, factors, multiples, and HCF/LCM.

Data Interpretation: Tables, charts, graphs, and data sufficiency.

By mastering these topics and practicing regularly, you can significantly improve your chances of scoring well in the Quantitative Aptitude section of the CAT exam.

[fortunatelycoldengineer]

What Does Big O(N^2) Complexity Mean?

It's critical to consider how algorithms function as the size of the input increases while analyzing them. Big O notation is a crucial statistic computer scientists use to categorize algorithms, which indicates the sequence of increase of an algorithm's execution time. O(N^2) algorithms are a significant and popular Big O class, whose execution time climbs quadratically as the amount of the input increases. For big inputs, algorithms with this time complexity are deemed inefficient because doubling the input size will result in a four-fold increase in runtime.

This article will explore what Big O(N^2) means, analyze some examples of quadratic algorithms, and discuss why this complexity can be problematic for large data sets. Understanding algorithmic complexity classes like O(N^2) allows us to characterize the scalability and efficiency of different algorithms for various use cases.

Different Big Oh Notations.

O(1) - Constant Time:

An O(1) algorithm takes the same time to complete regardless of the input size. An excellent example is to retrieve an array element using its index. Looking up a key in a hash table or dictionary is also typically O(1). These operations are very fast, even for large inputs.

O(log N) - Logarithmic Time:

Algorithms with log time complexity are very efficient. For a sorted array, binary search is a classic example of O(log N) because the search space is halved each iteration. Finding an item in a balanced search tree also takes O(log N) time. Logarithmic runtime grows slowly with N.

O(N) - Linear Time:

Linear complexity algorithms iterate through the input at least once. Simple algorithms for sorting, searching unsorted data, or accessing each element of an array take O(N) time. As data sets get larger, linear runtimes may become too slow. But linear is still much better than quadratic or exponential runtimes.

O(N log N) - Log-Linear Time:

This complexity results in inefficient sorting algorithms like merge sort and heap sort. The algorithms split data into smaller chunks, sort each chunk (O(N)) and then merge the results (O(log N)). Well-designed algorithms aimed at efficiency often have log-linear runtime.

O(N^2) - Quadratic Time:

Quadratic algorithms involve nested iterations over data. Simple sorting methods like bubble and insertion sort are O(N^2). Matrix operations like multiplication are also frequently O(N^2). Quadratic growth becomes infeasible for large inputs. More complex algorithms are needed for big data.

O(2^N) - Exponential Time:

Exponential runtimes are not good in algorithms. Adding just one element to the input doubles the processing time. Recursive calculations of Fibonacci numbers are a classic exponential time example. Exponential growth makes these algorithms impractical even for modestly large inputs.

What is Big O(N^2)?

An O(N2) algorithm's runtime grows proportionally to the square of the input size N.

Doubling the input size quadruples the runtime. If it takes 1 second to run on 10 elements, it will take about 4 seconds on 20 elements, 16 seconds on 40 elements, etc.

O(N^2) algorithms involve nested iterations through data. For example, checking every possible pair of elements or operating on a 2D matrix.

Simple sorting algorithms like bubble sort, insertion sort, and selection sort are typically O(N^2). Comparing and swapping adjacent elements leads to nested loops.

Brute force search algorithms are often O(N^2). Checking every subarray or substring for a condition requires nested loops.

Basic matrix operations like multiplication of NxN matrices are O(N^2). Each entry of the product matrix depends on a row and column of the input matrices.

Graph algorithms like Floyd-Warshall for finding the shortest paths between all vertex pairs is O(N^2). Every possible path between vertices is checked.

O(N^2) is fine for small inputs but becomes very slow for large data sets. Algorithms with quadratic complexity cannot scale well.

For large inputs, more efficient algorithms like merge sort O(N log N) and matrix multiplication O(N^2.807) should be preferred over O(N^2) algorithms.

However, O(N^2) may be reasonable for small local data sets where inputs don't grow indefinitely.

If you want more learning on this topic, please read more about the complexity on our website.

[roughentumble]

why are you introducing me to graphing quadratic functions, identifying vertexes, identifying minimums, identifying x and y intercepts, identifying the axis of symmetry, finding symmetric points, finding domain, finding range, AND making a chart FOR quadratic formulas, all in one single video without any breaks. im going to fucking kill you. mathhelp.com when i fucking gET YOU

[madrasahel1]

Understanding the EMSAT Math Syllabus: A Comprehensive Guide

The EMSAT Math syllabus is a crucial component for students preparing for the Emirates Standardized Test (EMSAT). This standardized test is designed to assess students' proficiency in various academic areas, and Mathematics is a significant part of the assessment. In this article, we will delve into the EMSAT Math syllabus, exploring its key components, the skills it aims to evaluate, and how Elmadrasah.com plays a pivotal role in helping students succeed in this examination.

Overview of the EMSAT Math Syllabus

The EMSAT Math syllabus is meticulously crafted to ensure that students possess the necessary mathematical skills and knowledge to excel in higher education and professional fields. The syllabus covers a broad spectrum of mathematical concepts, ranging from basic arithmetic to advanced topics. Understanding the EMSAT Math syllabus is essential for students aiming to perform well in the exam.

Key Components of the EMSAT Math Syllabus

Number and Algebra: This section includes fundamental concepts such as arithmetic operations, fractions, decimals, percentages, and algebraic expressions. Students are expected to demonstrate their ability to solve equations, understand inequalities, and manipulate algebraic expressions.

Geometry: Geometry topics in the EMSAT Math syllabus involve understanding shapes, sizes, and the properties of space. Students must be proficient in concepts such as angles, triangles, circles, and polygons. The ability to calculate area, volume, and surface area is also essential.

Statistics and Probability: This component focuses on the ability to interpret data, understand probability, and analyze statistical information. Students are required to work with various types of data representations, such as graphs and charts, and apply statistical measures to real-life scenarios.

Functions: Understanding different types of functions, including linear, quadratic, and exponential functions, is a key aspect of the EMSAT Math syllabus. Students should be able to interpret function graphs, solve function-related problems, and apply function concepts to various contexts.

Problem Solving and Reasoning: The EMSAT Math syllabus emphasizes critical thinking and problem-solving skills. Students are expected to approach mathematical problems methodically, use logical reasoning, and apply appropriate mathematical techniques to arrive at solutions.

The Role of Elmadrasah.com in EMSAT Math Preparation

Elmadrasah.com has established itself as a leading platform for educational resources and training. For students preparing for the EMSAT Math exam, Elmadrasah.com offers a range of services designed to enhance their understanding of the EMSAT Math syllabus and improve their performance. Here’s how Elmadrasah.com contributes to EMSAT Math preparation:

Comprehensive Study Materials: Elmadrasah.com provides detailed study materials aligned with the EMSAT Math syllabus. These resources include textbooks, practice problems, and interactive content that cover all key areas of the syllabus.

Online Courses and Tutorials: The platform offers online courses and tutorials specifically designed to address the EMSAT Math syllabus. These courses are taught by experienced educators who break down complex concepts into manageable lessons, making it easier for students to grasp challenging topics.

Practice Tests and Mock Exams: To help students assess their readiness for the EMSAT Math exam, Elmadrasah.com provides practice tests and mock exams. These practice assessments are designed to simulate the actual test environment, allowing students to familiarize themselves with the exam format and identify areas where they need improvement.

Personalized Tutoring: Elmadrasah.com offers personalized tutoring sessions for students who require additional support. Tutors work closely with students to address their specific needs, providing targeted instruction and feedback to enhance their understanding of the EMSAT Math syllabus.

Interactive Learning Tools: The platform features interactive learning tools that engage students and make learning more effective. These tools include video lessons, quizzes, and educational games that reinforce key concepts from the EMSAT Math syllabus.

Expert Guidance and Support: Elmadrasah.com’s team of experts provides guidance and support throughout the preparation process. From answering questions to offering study tips, the support team helps students stay on track and build confidence in their mathematical abilities.

Progress Tracking and Feedback: To ensure that students are making progress, Elmadrasah.com offers tools for tracking performance and providing feedback. Students can monitor their progress, review their strengths and weaknesses, and adjust their study strategies accordingly.

Resourceful Blog and Articles: Elmadrasah.com maintains a blog with articles and resources related to EMSAT Math preparation. These articles offer valuable insights, study tips, and updates on changes to the EMSAT Math syllabus.

Community and Forums: The platform hosts forums and community groups where students can connect with peers, share experiences, and seek advice. Engaging with a community of learners can provide additional motivation and support.

Flexible Learning Options: Recognizing that students have diverse learning needs, Elmadrasah.com offers flexible learning options. Whether students prefer self-paced learning or structured courses, the platform provides resources and support to accommodate different preferences.

Conclusion

The EMSAT Math syllabus encompasses a wide range of mathematical concepts and skills that are crucial for academic and professional success. Understanding the syllabus and preparing effectively are key to achieving a high score in the exam. Elmadrasah.com plays a significant role in supporting students through comprehensive study materials, interactive learning tools, and expert guidance. By leveraging the resources and services offered by Elmadrasah.com, students can enhance their preparation, build confidence, and increase their chances of excelling in the EMSAT Math exam.

[math-journal2]

Algebra 2 - here - Book Ed1

Precalculus 1

Book: Precalculus 2e, Abramson, Jay, OpenStax, 2021

Transformations / Trig Review + 7.1

Unit 1

Review / Algebra 2 Cheat Sheet

Parent Function: D & R

Set Builder Notation

Piecewise Function

^Tough Example I x I

Unit 2

Function Operations

Decomposing

Composites

Inverse Function

Review

Unit 3 [Book Notes]

Parabola Basics

Switching Between Formats

Quadratic Word Problem

Imaginary numbers

#imaginary review

Complex Conjugate Solving

Complex Plane / Solving i^#

Power Function (3rd degree +)

Graphing Polynomials (pg1)

*Power function is a format of polynomials

Unit 3 [Class Notes]

Imaginary / Quadratic Formula

Polynomial Functions (include end behavior and D/R)

Note: there weren’t any word problems on the quizz. Also solving for a (sub n) was a significant part. Plus, make sure to write x-intercepts as ordered pairs.

Unit 4 [Book Notes]

Dividing Polynomials

Long Division

Synthetic Division

Word Problem

Finding Zeros

Remainder Theorem

Basic poly division

Factor Theorem

Poly division, factor, solve for x

Rational Zero Theorem

Find possible x-intercepts or zeros

Finding Complex Zeros

^ same, a>0

Unit 4 [Class Notes]

Long D v Synth D

Eq —> Zero, Zero —> Eq

Possible Zeros, p/q

Narrow Possible Zeros

Graphing always option

Complete Factorization

Sq Root Zero —> Eq, Vertex Form

Terminology

Complex Zero Dump

MID TERM REVIEW

Unit 5

1/x

Rational Functions

Graphing

Edit: D > N —> y=0 h.a.

D < N —> y = slant

D = N — y= a/b

Exponent

Decay and Growth

Graphing

Extra

Application Problems

Compound Interest v Continuous Growth

Logs

Common v Natural

Algebra 2 Solutions

Graphing Logs

UNIT REVIEW

*note: no interpretting graphs on quiz

.

Unit 6

Log/Exponent Rules

Expanding Logs

Ways to Solve

Application Problems

Graph —> Eq

No review

Hard part: solving exponents of different bases / richter scale application problem / decibel / newton’s law of cooling

.

Unit 7

Basic Circle

Circle Problems

NonStandard —> Standard

Ellipses

Parabola

*my book notes are a mess, so yeah… ignore them. Only listing classnotes on MP

UNIT REVIEW

[prashantgujjar]

What would be the equation of the following surface?

 I have the raw data of X, Y, Z, where X and Y are inputs and Z is the output. Plotting the surface gives the red curve in the below picture:

The surface seems to be a simple function involving trigonometric functions. For example, plotting the equation cos(X)^2 + cos(Y)^2 gives the blue surface and it looks similar to the red graph (but the RMS error is very large).

I have tried introducing variables (a1*cos(X)^2 + a2*cos(Y)^2), where a1 and a2 vary from 0 to 1) but the RMS error is still large.

I also tried the surface fitting functions (MATLAB's fit function) but it's models are limited (unlike the curve fitting models which include Fourier series, sin series, etc).

How can I find the equation which gives the red surface?

Edit for clarity: I am able to use the lsqcurvefit (or any other curve fitting toolbox functions) to find which coefficients to use, but I am not sure what the equation should be. cos(X)^2 + cos(Y)^2, for example, is not the right equation but it does have a similar shape.

If this seems improbabilistic, how can I vary cos(X)^2 + cos(Y)^2 to align the end curves of the surface (where there seems to be highest misalignment)?

NOTE:-

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Update 3: Added some surface plots.[X, Y] = meshgrid(-1:0.05:1); %% Polynomial function c = 1; b = 1/2; a = b; Z = c - b*Y.^2 - a*X.^2; % can try higher-order polynomial functions surf(X, Y, Z), grid on title('Quadratic function'), xlabel x, ylabel y, zlabel f(x,y)

SEE COMPLETE ANSWER CLICK THE LINK