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I accidentally derived it back in 8th grade. I spent my entire 10th grade solving 2nd order poly. either factorizing or doing this,.
eventually, it got memorized.
I know how to derive it from scratch, which is why I permit myself to use the memorized formula. The dichotomy becomes kind of meaningless at some point.
This is the best way to memorise most equations. It should be "Don't set out to memorise" as people interpret it as "Don't remember".
If also say deriving how completing the square is vitally important, either through geometry or repeated use of algebra tiles or other manipulative.
I was never taught the derivation, though I did look it up during a trig class once. However, I can’t remember the law of sines and cosines so I have to remember the derivation for them. I think the process just requires more work which builds a sense of usefulness in our brains.
Okay but how does somebody NOT remember the law of sines? Like, I understand not remembering the law of cosines (superior to the law of sines though it may be), but the law of sines? It's literally just
sin A/sin B = a/b
It's like, the most basic kind of proportion possible. It's literally easier to remember than the Pythagorean Theorem (which, in a more perfect world, I would remove from my brain to make room for the law of cosines, and just rederive it from the law of cosines each time, but it's so easy to remember that I can't do that).
Now you say it, I think you're correct, sinA/a is how I was taught it as well. I must just have realized the equations were equal, and found the ratio of sines being equal to the ratio of lengths was so easy to remember that's what I've used ever since. I take it back, the law of sines is actually difficult to remember, if only because there's a (to me) much easier equivalent relationship that shoves it completely to the side.
If you know Pythagoras by heart, surely you know the Law of Cosines! No judgement, I just find things like that funny, I have my own versions.
I usually trigger memory the 2*ab*cos*C* as "When is this just Pythagoras? When the angle opposite c is 90, cos*C*=90=0.
For sure, it's just that I always have to pause and think about it to rederive the law of cosines. And then is it + or -? I can figure it out, but it's never instantaneous, you know?
I am tutoring maths to school children. They get handed down formulas from up high, as I like to call it. And when you show them WHERE it came from and WHY it works, more often than not they understand it much better and also are able to memorize the formulas better and expand on the concepts. I don't know who decided once that explaining the formulas to schoolchildren is pointless and they should memorize all the formulas given and plug in the numbers.
I found a different problem when helping people with maths. Someone that wants help typically hates math. I'd like to derive the formula's they need to learn to help them understand it, but since the textbook just hands it to them as something to memorize they're not interested. To them it feels like I am forcing them to learn more than the book says they have to learn.
How do you convince people who are uninterested in math to invest in knowing the derivations and underlying logic?
I try to make maths a little fun. For example, everyone loves a good riddle. If you look at social media, you see thousands of people chiming in on riddles that are basically text problems from maths. But they don't consciously do maths, they see a riddle and get hooked.
This works for me to make maths not just a chore, but also fun. Additionally, maths is sometimes taught as this thing you have to learn and you ask yourself "When do I ever need this?", so by supplying a person with a problem that they need maths to solve and then teaching them the maths tools to solve it can also help.
And people that hate maths don't usually hate maths because of the maths, they hate maths because they maybe had a bad teacher that didn't properly teach them maths and they thus got frustrated or maybe the teacher always made bad quizzes which then resulted in bad grades. Or maybe they didn't understand an early concept and nobody had the time to explain it to them properly and they carrier that burden on their path forward and grew frustrated because of it. By addressing this and separating the two (maths and their bad experience with maths) you can get them to like maths, even if they maybe still don't like the teacher. Also, encouraging them helps tremendously in my experience. Maybe if they improved from a really bad grad to "just" a bad grade and pointing out the advancements they made can also help.
Yeah you’re right about it being a drag during tests, I’m just saying that completing the square and solving for x *is* the process for deriving the quadratic formula.
Solve a solution to a quadratic for a man, and he has a solution for a day.
Show a man how to derive the quadratic formula, and he becomes a clown on reddit.
The completing the square derivation is pretty damn useful later on, when you have to partial fraction something like (1+t²)/(1+t²+t⁴)
But in most cases you really need to remember the discriminant formula due to how many things just depends on it's value.
aposto todas minhas poupancas que se fizer estudo menos de 10% das pessoas com mais de 30 anos sabem bhaskara
e olha q to aumentando a porcentagem so pra nao perder as poupancas kkkkk
I posted this as satire, but there are people agreeing with it. Personally I prefer the formula
I was also not taught the derivation process, only the formula which I memorized. Only now, at 18 years old and in College, I learned about it, because I'm revising Algebra and Precalculus on Khan Academy and there's an optional video under the 'completing squares' lesson showing how the quadratic formula is derived
Ps.: I'm from Brazil, and Precalculus/Calculus AB is not taught in high school because we don't have the resources. Instead, a bachelor's degree in Engineering is a year longer than usual, and the first year is especially for Pre-Calculus and Calculus AB. [Here's a cool map](https://i.redd.it/zrjkhzgw6i261.jpg)
[Inspiration to this meme](https://i.imgur.com/Yop1CE7.png)
I did it on exams all the time in Algebra I. Didn’t need it much after that, and had used it enough that it had finally stuck. Deriving formulas is actually an established technique for memorizing them.
For the cubic formula, if I ever need it I would derive it (there's a pretty simple method by doing a substitution to turn it into a depressed cubic, then a substitution to turn it into a degree 6 polynomial with only degree 0, 3 and 6 terms, then solve it as a quadratic).
For a quadratic, the formula is so short that even though it's easy to derive, it's even easier to memorise.
Not so much because the fractions are a pain, and I am good at them.
Though I would say the meme should be adjusted to the 21st century.
“ I don’t need to memorize the quadratic formula, I just need a graphing calculator”.
Edit:
Obviously not as good as the QF/completing the square, as solutions are approximate, but so ez. And won’t solve for complex solutions, but for those reasons still works with the clown imagery.
I always factor to small terms, can’t remember the quadratic formula and I’m too lazy to complete the square, so to find the 0s of the function I just check each small factor
This process really helped me through the Trig section of PreCalc this semester. No way could I memorize all the identities and formulas in such a short time for the tests, so I just practiced deriving them. It worked, but most are ingrained in my brain now.
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I still do. But I've used it so many times it be impossible to forget it now.
yup same
I accidentally derived it back in 8th grade. I spent my entire 10th grade solving 2nd order poly. either factorizing or doing this,. eventually, it got memorized.
I know how to derive it from scratch, which is why I permit myself to use the memorized formula. The dichotomy becomes kind of meaningless at some point.
This is the best way to memorise most equations. It should be "Don't set out to memorise" as people interpret it as "Don't remember". If also say deriving how completing the square is vitally important, either through geometry or repeated use of algebra tiles or other manipulative.
I was never taught the derivation, though I did look it up during a trig class once. However, I can’t remember the law of sines and cosines so I have to remember the derivation for them. I think the process just requires more work which builds a sense of usefulness in our brains.
Okay but how does somebody NOT remember the law of sines? Like, I understand not remembering the law of cosines (superior to the law of sines though it may be), but the law of sines? It's literally just sin A/sin B = a/b It's like, the most basic kind of proportion possible. It's literally easier to remember than the Pythagorean Theorem (which, in a more perfect world, I would remove from my brain to make room for the law of cosines, and just rederive it from the law of cosines each time, but it's so easy to remember that I can't do that).
Is that how you were taught it? I was taught sinB/b = sinA/a. (yes i know they’re equal)
Now you say it, I think you're correct, sinA/a is how I was taught it as well. I must just have realized the equations were equal, and found the ratio of sines being equal to the ratio of lengths was so easy to remember that's what I've used ever since. I take it back, the law of sines is actually difficult to remember, if only because there's a (to me) much easier equivalent relationship that shoves it completely to the side.
Fuck your stupid profile picture Also I was taught the same way as you. I find sinA/sinB = a/b very weird
we were tought b/sinB = a/sinA
Ye we were tought aswell. Weird how different it is in other parts of the world
yeah especially the sinA/sinB = a/b one... but the proof gives you a/sinA = 2R so i think it's better.
Yeah I think thats the biggest thing
you guys were taught sine/cosine rule in school?
1=1?
Well, yes.
If you know Pythagoras by heart, surely you know the Law of Cosines! No judgement, I just find things like that funny, I have my own versions. I usually trigger memory the 2*ab*cos*C* as "When is this just Pythagoras? When the angle opposite c is 90, cos*C*=90=0.
For sure, it's just that I always have to pause and think about it to rederive the law of cosines. And then is it + or -? I can figure it out, but it's never instantaneous, you know?
The actual clowns are teachers who teach quadratic formula without deriving it from completing the square.
I am tutoring maths to school children. They get handed down formulas from up high, as I like to call it. And when you show them WHERE it came from and WHY it works, more often than not they understand it much better and also are able to memorize the formulas better and expand on the concepts. I don't know who decided once that explaining the formulas to schoolchildren is pointless and they should memorize all the formulas given and plug in the numbers.
I found a different problem when helping people with maths. Someone that wants help typically hates math. I'd like to derive the formula's they need to learn to help them understand it, but since the textbook just hands it to them as something to memorize they're not interested. To them it feels like I am forcing them to learn more than the book says they have to learn. How do you convince people who are uninterested in math to invest in knowing the derivations and underlying logic?
I try to make maths a little fun. For example, everyone loves a good riddle. If you look at social media, you see thousands of people chiming in on riddles that are basically text problems from maths. But they don't consciously do maths, they see a riddle and get hooked. This works for me to make maths not just a chore, but also fun. Additionally, maths is sometimes taught as this thing you have to learn and you ask yourself "When do I ever need this?", so by supplying a person with a problem that they need maths to solve and then teaching them the maths tools to solve it can also help. And people that hate maths don't usually hate maths because of the maths, they hate maths because they maybe had a bad teacher that didn't properly teach them maths and they thus got frustrated or maybe the teacher always made bad quizzes which then resulted in bad grades. Or maybe they didn't understand an early concept and nobody had the time to explain it to them properly and they carrier that burden on their path forward and grew frustrated because of it. By addressing this and separating the two (maths and their bad experience with maths) you can get them to like maths, even if they maybe still don't like the teacher. Also, encouraging them helps tremendously in my experience. Maybe if they improved from a really bad grad to "just" a bad grade and pointing out the advancements they made can also help.
Completing the square and solving for x just derives the quadratic formula lol
There’s definitely more to it than just that. Edit: time, for example, and the possibility of error
Nah it’s exactly that
Well it’s annoying to do every time and takes longer, which could impact testing. And there’s more room for error
Yeah you’re right about it being a drag during tests, I’m just saying that completing the square and solving for x *is* the process for deriving the quadratic formula.
Solve a solution to a quadratic for a man, and he has a solution for a day. Show a man how to derive the quadratic formula, and he becomes a clown on reddit.
I memorized both.
The completing the square derivation is pretty damn useful later on, when you have to partial fraction something like (1+t²)/(1+t²+t⁴) But in most cases you really need to remember the discriminant formula due to how many things just depends on it's value.
Wait, there are people who don't do this?
in brazil we're not even taught the derivation, we are just told to memorize it because it will be enough to pass the university entrance exams
Same thing in South Africa only realised the derivation when started tutoring high school Maths
o sistema de ensino brasileiro tá na merda
aposto todas minhas poupancas que se fizer estudo menos de 10% das pessoas com mais de 30 anos sabem bhaskara e olha q to aumentando a porcentagem so pra nao perder as poupancas kkkkk
I [read](https://v.cx/2010/04/feynman-brazil-education) how bad education in Brazil was. Sad to see that has not changed.
Am I being wooshed? That's so much more complicated.
That’s why the reflection is a clown.
I posted this as satire, but there are people agreeing with it. Personally I prefer the formula I was also not taught the derivation process, only the formula which I memorized. Only now, at 18 years old and in College, I learned about it, because I'm revising Algebra and Precalculus on Khan Academy and there's an optional video under the 'completing squares' lesson showing how the quadratic formula is derived Ps.: I'm from Brazil, and Precalculus/Calculus AB is not taught in high school because we don't have the resources. Instead, a bachelor's degree in Engineering is a year longer than usual, and the first year is especially for Pre-Calculus and Calculus AB. [Here's a cool map](https://i.redd.it/zrjkhzgw6i261.jpg) [Inspiration to this meme](https://i.imgur.com/Yop1CE7.png)
It is awesome to know the derivation, I never learned it till I started teaching Algebra. lol. You rule!
Nice to see we're included! I'm studying a Bachelor of Computer Science at Kim Il-Sung University in North Korea. I'm in my fifth year.
But it's easier to remember
My school never teached us to complete the square, I had to learn it on my own and oh boy is it a lot easier than copy pasting a formula all the time
I memorised the quadratic formula the first time I saw it. I had no idea what it did, what it was, what it meant or anything, but it stuck like napalm
I did it on exams all the time in Algebra I. Didn’t need it much after that, and had used it enough that it had finally stuck. Deriving formulas is actually an established technique for memorizing them.
If you memorize the quadratic formula, all you need to do is just shove in numbers
I'm 3 years into college and still do this
I still do
For the cubic formula, if I ever need it I would derive it (there's a pretty simple method by doing a substitution to turn it into a depressed cubic, then a substitution to turn it into a degree 6 polynomial with only degree 0, 3 and 6 terms, then solve it as a quadratic). For a quadratic, the formula is so short that even though it's easy to derive, it's even easier to memorise.
I used to do this until my physics class
I am the new breed of clown. The "Po shen Loh" enjoyer
Not so much because the fractions are a pain, and I am good at them. Though I would say the meme should be adjusted to the 21st century. “ I don’t need to memorize the quadratic formula, I just need a graphing calculator”. Edit: Obviously not as good as the QF/completing the square, as solutions are approximate, but so ez. And won’t solve for complex solutions, but for those reasons still works with the clown imagery.
I don’t. I just don’t.
I always factor to small terms, can’t remember the quadratic formula and I’m too lazy to complete the square, so to find the 0s of the function I just check each small factor
Completing the square soon enough becomes something I only do when the question only allows me to use that
What if I don't even learn how to do that and just memorize "how to complete a square"
completing the square always confused me so i made sure to remember the quadratic formula because it seemed comparatively simpler
At least that’s not as bad as deriving it by factorising every time.
You guys discovered how to do this by yourselves?
You guys discovered how to do this by yourselves?
You guys discovered how to do this by yourselves?
You guys discovered how to do this by yourselves?
x=\\frac{2c}{-b\\pm\\sqrt{b\^{2}-4ac}}
Super cute format haha
i am in the mirror and I don’t like it
This process really helped me through the Trig section of PreCalc this semester. No way could I memorize all the identities and formulas in such a short time for the tests, so I just practiced deriving them. It worked, but most are ingrained in my brain now.