Finding a non-linear equation from a set of points

Question

I'm trying to figure this out and I need help.

I have a set of points and I know they are quadratic because the differences between the y points aren't the same.

But how do I find the equation of a nonlinear equation?

X | Y

-2 | -1

-1 | -4

3 | 4

4 | 11

Answer 1

First you posit a quadratic equation in unknowns a, b, c thus: Y = a$X^2$ + b$X$ + c. Now plug in your five X and Y values, yielding five (linear!) equations in a, b, c. Solve for a, b, c (I assume you know how to solve linear equations in three unknowns).