Answer
$2x^2-16x+24$
Work Step by Step
When the vertex of a graph is at $(h,k)$, then the general formula for the quadratic function is $f(x)=a(x−h)^2+k$.
As depicted in the picture, the vertex of the graph is at
$(h,k)=(4,-8)$
So, the quadratic function becomes:
$f(x)=a(x−4)^2−8$.
Since, the point $(0,24)$ is on the graph, plugging into the above equation gives:
$24=16a-8 \implies a=2$
Thus, $f(x)=2(x−4)^2−8=2(x^2+16-8x)-8=2x^2-16x+24$