# Least Squares Parabola

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Last edited:

#### Dragan

##### Super Moderator
Hi all

I have been trying to find the values of the coefficients for the least squares parabola:

y = a + bx + cx^2

I have taken partial derivatives wrt a, b, c and now have three equations, but I don't know what to do next...any suggestions? Have you solved this before?

thank you very much!!

I can help with LaTeX in exchange for help thank you very much

Your system of normal equations should look like the following:

$$\Sigma y=an+b\Sigma x+c\Sigma x^{2}$$

$$\Sigma xy=a\Sigma x+b\Sigma x^{2}+c\Sigma x^{3}$$

$$\Sigma x^{2}y=a\Sigma x^{2}+b\Sigma x^{3}+c\Sigma x^{4}$$

#### Dason

##### Ambassador to the humans
It's a system of three equations with three unknowns (a, b, c). Everything else is taken as a known fixed value. If I told you to solve for a, b, c given the following equations could you do it?

1 = 3a + 4b - 2c
2 = 7a - 13b + 8c
92 = a + b - c