"How Did You Memorize The Quadratic Equation?"

"How are you so smart?"

Guess where I am right now:
A. Elementary School
B. Middle School
C. High School
D. College

'MURICA

Sing it to the tune of 'Pop goes the weasel'.

NO NEED

I have a degree in mathematics and I still can't remember the derivative quotient rule without (a.) proving it directly from the limit definition of the deriviative of 1/g(x) or (b.) singing it to the tune of "If You're Happy And You Know It."

So if you hear me clapping in the middle of an analysis exam, you know exactly what the *** I'm up to.

Yeah screw quotient rule I just make it into an inverse product.

It's funny because when you actually PROVE that the quotient rule works in upper level math courses, that's what you do.

"Well ***, you mean that thing I did for all these years to avoid using the quotient rule was the proof of the quotient rule!?"

Also *** I didn't know the pop goes the weasel mnemonic for the quadratic equation.

Tutoring freshmen will never be the same.

You know while you may look down on the person asking that question. You have to think. Could they being going into a career that they'll never use such knowledge? If so what would be the point? I know you look at it as basic knowledge but many wouldn't. The basic knowledge they seek and thrive in is that that they'll use everyday in the working class. There is nothing wrong with that at all and is very much needed in today's society. To look down on someone who didn't know or is impressed with your knowing is more shameful than them not knowing.

Also before Sylow bites my head off... Math is awesome and needed as well. :)

Actually, the question was how did you memorize the quadratic equation.

If this person has trouble memorizing simple things I hope they end up in a job far away from any field where other peoples' lives will be subject to the quality of their work.

You'd be surprised with how many such jobs exist. Cashier(with automated systems), Stocking, ranch/farm hands, trash men, etc. While not the leading force of society they still fill gaps that are needed. Though with this person being in college (possibly?). I could see a problem if they're seeking higher than they should.

Trash man is one of the occupations in the US with the highest mortality rates, I believe agricultural jobs are up there as well.

Really? I wouldn't have expected that tbh.

Edit: I could understand ag though. I almost had a pig bite my hand off the other day; mean little ***.

Repetiton.

Forgot if it was AlgebraII or Math Analysis, back in 1995-96', but when you have to use it over and over for the coordinates to make an ellipse you memorize it pretty quick.

I agree, repetition

Answer to the question: I didn't.

Reference: "How do you spell 'obfuscate'?" "I don't."

Einstein said never to memorize something that can be easily looked up. Memorizing the atomic weight of cesium is pointless as long as periodic tables exist and that's even more true these days with electronic references. Assuming you're capable of figuring out the equation from first principles, which any competent mathematician could do, why memorize it when a computer will sort it out with a single click?

On the flipside, though, if you need a mnemonic for something that you either a.) use all the time or b.) should understand intuitively, you may have a problem. Anyone over the age of 15 who needs a mnemonic to remember mathematical order-of-operations, for instance, should probably be kept in a padded room wearing a helmet. That may just be my prejudice speaking, though, because outside of MMO mechanics, I can't remember the last time I actually used order-of-operations for anything.

Its like tying a shoe.. after a while you dont even think about it. I use to write on top of every page of my hw i would do that needed it. After a while i didnt need to write it since it was stuck in my head.

you are the most pretentious poster these forums have ever seen

also, you don't have to 'need' a mnemonic to benefit from it

in this particular case i remember my elderly teacher singing it in middle school because 11-year-old me thought it was funny.. haven't used it recently and certainly wouldn't be able to pull it out of my memory if that hadn't happened

Define "pretentious."

"characterized by assumption of dignity or importance, especially when exaggerated or undeserved"

in your case, indicated by the tone of condescension in every post you make

How "Ostentatious"!!

Condescension and pretentiousness are not synonymous. They're barely even related.

If you want to call me a condescending ***, do so. It would be true. I'll follow that by pointing out that you're the one who suffers from undeserved self-importance, as evidenced by making a false equivalency between the utility of a fact and random nostalgia associated thereto.

Also, using the word "pretentious" to mean "something I don't like" is rather pretentious in and of itself and, indeed, one of the reasons why I don't use the word. It's something like Godwin's Law, really.

Endocrinology was the only class I had to drop for the preservation of my own mental well-being.

point proven

I suffered through it and then moved on to behavioral endocrinology which was basically graduate level sex ed.


worth it.

Is it odd that I have a liberal arts background and am not mystified by endocrinology? I mean, I really should be, but every time I read up on it, it weirdly makes sense.

Use the logarithmic derivative, then the product and quotient rules become nothing more than extensions of the chain rule.


Edit for example:


Example)

d/dx[(x^2)/(sin(x))]

Recall:

d/dx{ln(f(x))] = (f'(x))/(f(x))

Let f(x) = (x^2)/(sin(x))

Then,

d/dx[ln(f(x)] = d/dx[ln((x^2)/(sin(x))] =

d/dx[ln((x^2)) - ln((sin(x))]=

d/dx[ln((x^2))] - d/dx[ln((sin(x))].

Using the above for the derivative of a logarithm we have:

d/dx[ln((x^2))] = (2x)/(x^2)

and

d/dx[ln((sin(x))] = (cos(x))/(sin(x)).

Thus,

d/dx[ln((x^2)/(sin(x))] =

(f'(x))/(f(x)) = ((2x)/(x^2)) - ((cos(x))/(sin(x))).

Multiply through by f(x) yields:

f'(x) = ((x^2)/(sin(x))) * ((2x)/(x^2)) - ((cos(x))/(sin(x))).

Simplify:

f'(x) = ((2x)/(sin(x))) - ((x^2)(cos(x))/(sin^2(x)))=

((2x)(sin(x))/(sin^2(x))) - ((x^2)(cos(x))/(sin^2(x)))=

((2x)(sin(x))-(x^2)(cos(x)))/(sin^2(x)).

From which it can easily be seen for p(x)/q(x)

d/dx[p(x)/q(x)] = ((p'(x)*q(x))-(p(x)*q'(x)))/((q(x)^2)).

The same reasoning can be used to do a product as well using the property ln(xy) = ln(x) + ln(y).

This method provides a demonstration of why the product and quotient rules work the way they do. Are there more steps? for sure. However, the method is VERY mechanical assuming you can remember d/dx[ln(f(x))] = f'(x)/f(x).

Further it is far more powerful. For example it lets us take derivatives of functions like:

f(x) = 2^(-x).

This function does not submit to any of the fundamental rules of calculus. Unfortunately, you do not come across the logarithmic derivative, I believe, until you discuss the argument principal in complex analysis.


As for the OP:

Just memorize it...make a flash card and repeat it to yourself all the time. Work through exercise problems where you use it. The quadratic equation is something you will never stop using in mathematics. Knowing the zeros of a function is a very important a property to know. It may be helpful to look up some proofs of the quadratic equation, Wikipedia may have a couple, so that it makes more intuitive sense to you. Then, since you understand what everything means, it isn't memorization but rather a conclusion based on facts you already know.

I knew you reminded me of someone I couldn't put my finger on, and I finally realized it's Elanabelle.