Lorin seems to think that I'm some kind of math whiz because I've been getting good grades in Calculus, while in reality it's a real struggle for me to understand all of the amazing math that other people have figured out. Through all the formulas and proofs I first try to understand why it works, sometimes I can and sometimes it's beyond me so in those cases I just try to understand how to use it properly so I can get the right answers!
One basic formula that I first learned before I cared about "why it works" is the quadratic formula. I just accepted it at the time and have used it since then. Now that I'm thinking more deeply about such things, I feel a little guilty every time I use it, like I'm copying someone else's homework. Well today I put a stop to the guilt, I decided to derive it without looking at a proof.
I know most of you probably don't care too much about this but Lorin was asking if my blog is about math, no it's not a math blog but I'll do this one post for him. So here it is Lorin, an old favorite and a standard of elementary Algebra: The Quadratic Formula. Use it to impress people at parties!
First factor out the coefficient of the x^2 term, you can immediately eliminate it by dividing both sides by it (for some reason I kept it around till the next step in my work). Then you must do the dreaded "complete the square" technique, I was feeling a little bold today so I did a few steps in my head on this one. Then it's just a matter of isolating x, get rid of the square by taking the square root of both sides (don't forget your plus/minus) and simplify. My circuits teacher recently used the quadratic equation in a different form as noted in the figure, the reason why he likes it is because of the repeated b/2a term. I had never seen it like that before but now I see where it comes from.
