Use the inner product $$\langle f,g\rangle = f(-3)g(-3) + f(0)g(0) + f(2)g(2)$$ in $P_2$ to find the orthogonal projection of $f(x) = 2 x^2 + 5 x + 9$ onto the line $L$ spanned by $g(x) = 3 x^2 - 5 x + 4$.

${\rm proj}_L(f) =$ .