There is a valley that is elevated 9% on the left side and 6% on the right side. Point A is located on the left and point B on the right. The distance between A and B is 1000 ft.

How do i find the quadratic function y=ax^2 + bx +c for the interval -500<x<500 that describes the top of the filled region.

I know derivative are involved somehow but other than that I;m lost.
Any help??