"How Did You Memorize The Quadratic Equation?"

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"How did you memorize the quadratic equation?"
 Odin.Godofgods
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By Odin.Godofgods 2013-12-06 04:14:56
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behemuthxero said: »
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)).

There was a time where i could follow that fairly easily... Now i think it looks remarkable similar to Chinese script /grin :(
 Phoenix.Dabackpack
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By Phoenix.Dabackpack 2013-12-06 17:39:32
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Don't think you're stupid or anything if you're having trouble memorizing something like this. Everyone has their things they're good at and bad at.

I'm a junior Math/CS double major and have been excelling in my math/CS courses but this semester I'm literally failing my Numerical Analysis classes. It's just something I have a low affinity with, I guess :( But that doesn't mean I'm "bad at math".

As for the Quadratic Formula, I just used it enough in middle school and now I use it almost every other day. Repetition really works wonders.
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By fonewear 2013-12-06 17:51:44
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Bismarck.Ihina said: »
"How are you so smart?"

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

'MURICA

On that crazy Planet of the Apes I've been hearing about ?
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By Rebo Stormborn 2013-12-06 19:47:36
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Fighting Irish Theme Song: X = negative B... plus or Minus the square root of..B-Squared - 4ac all over 2 times A Hurray!

This is how my math teacher taught it to us in 8th grade.
 Lakshmi.Saevel
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By Lakshmi.Saevel 2013-12-06 21:49:43
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I used to have all that stuff memorized and thought those who didn't were dumb. Then I left school and got into the real world and realized that 99% of that is useless on a day to day basis. It's good to know the concept and be capable of understanding the implications and relationships involved, but to actually have such things memorized is a waste. You won't be using it and it'll eventually drift away.

The only profession I've seen that actually use's that on a daily basis are EE's and ME's. Academicians don't count.
 Fenrir.Sylow
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By Fenrir.Sylow 2013-12-06 21:53:01
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I think the key thing most people are glossing over is that the OP is implying that the asker is bewildered by the idea of having memorized a formula, and then equating having memorized it with being "smart." That's the problem here, not the fact that they don't remember the quadratic formula.
 Shiva.Jirachi
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By Shiva.Jirachi 2013-12-06 21:54:49
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To answer your question, because you said "'Merica" I would imagine Middle School.

To Asnwer the thread name topic, my Algebra 2 teacher had a song.
Annoying however it stuck in my head. Here is a smilliar version.
 Shiva.Onorgul
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By Shiva.Onorgul 2013-12-06 22:05:29
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I just remembered why I immediately forgot this equation after I finished Algebra II in high school: I don't remember any practical use for it.

I used the concepts behind derivatives and integrals to improve my driving ability after I got my license. I use inverse proportions to convert recipes. I never had any use for it, but I was at least fascinated by the way a sine wave is formed. But all those parabola equations never seemed to translate into something fungible. Any math-types feel like tackling this?
 Bismarck.Hsieh
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By Bismarck.Hsieh 2013-12-06 22:36:24
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Flash cards or practice. There is no need to derive it because your teacher will probably won't care or give you more points for it.
 Siren.Calnus
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By Siren.Calnus 2013-12-06 23:44:37
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My teacher tried to implant that pop goes the weasel method. I guess it works but Jesus that was annoying. For once I couldn't last minute or not study and improvise. Math is my major weak point and it's a miracle I passed all my college math with a B.

Find any method and just beat it into your head until insanity kicks in.
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