Answer
$f(x)=-3(x-2)^2-4$.
Work Step by Step
If the vertex of a graph is at (m,n) then the general formula for the quadratic function is $f(x)=a(x-m)^2+n$. The vertex of the graph is at (2,-4), hence the quardatic function becomes $f(x)=a(x-2)^2-4$. The point (0,-16) is on the graph (because of the y-intercept), hence if we plug in the values we get -16=4a-4, hence a=-3, hence $f(x)=-3(x-2)^2-4$.