Find the parabola of the form $y=ax^2+b$ which best fits the points $(-1,0)$, $(4,4)$, $(5,8)$ by minimizing the sum of squares, $S$, given by $$S=(a+b)^2+(16 a+b - 4)^2+(25 a+b- 8)^2.$$

$y =$ $x^2 +$