Use the inner product f g f2g2 f0g0 f2g2 in P2 to find th

Use the inner product (f, g) = f(-2)g(-2) + f(0)g(0) + f(2)g(2) in P_2 to find the orthogonal projection of f(x) = 4x^2 + 4x + 7 onto the line L spanned by g(x) = 2x^2 - 2x - 9. Proj_L(f) =

(f,g) = f(-2)g(-2)+f(0)g(0)+f(2)g(0)
= [{4(-2)^2+4(-2)+7}{2(-2)^2-2(-2)-9}]+[{4(0)^2+4(0)+7}{2(0)^2-2(0)-9}]+[{4(2)^2+4(2)+7}{2(2)^2-2(2)-9}]

= (15*3)+63+(31*-5)
= -263