Quadratic Regression (Least Squares)

I've done my best to try and find the 3 formulas for a least squares quadratic regression. I remember doing this in my first year of engineering school. I think it was the first all-nighter I pulled. Here's how it goes:

Error = sum((yi-(ax^2+bx+c))^2)

dE/da = 0
dE/db = 0
dE/dc = 0

This leads you to three equations and three unknowns. It doesn't sound hard, but the algebra is so complex, it's nearly impossible.

You come out with three formulas, one for each of the three constants of the quadratic (ax^2 + bx + c). These formulas are in terms of summations of your measured y and x values and in terms of the total number of measurements you have.

I'm going to look for my notes from the first engineering class, and if I can't find them, I'll try to use the simplify function of MathCad or the TI-89.


I know you can't wait for me to find the equations and to post them.