Answer
$f(x)=2(x-4)^2-8$.
Work Step by Step
If the vertex of a graph is at (m,n) then the general formula for the quadratic function is $f(x)=a(x-m)^2+n$. According to the picture the vertex of the graph is at (4,-8), hence the quadratic function becomes $f(x)=a(x-4)^2-8$. The point (0,24) is on the graph, hence if we plug in the values we get 24=16a-8, hence a=2, hence $f(x)=2(x-4)^2-8$.
