Urgent! a problem related to Numerical Analysis!!!?

[Nate]

Let the weight function w be symmetric with respect to the center c of (a, b), i.e. w(x) = w(2c - x) for all x belongs to (a, b). show that if f is also symmetric with respect to the center f(x) = f(2c - x) then the polynomial Pn that is the best least approximation to f is also symmetric.

any suggestions??? thanks a bunch

[ProblemSolver]

if linear or quadratic (or even) it (Pn) would be symmetric.