Answer
$f(x)=-2(x+2)^2+6$
Work Step by Step
If the vertex of a graph is at $(m,n)$ then the vertex form for the quadratic function is $f(x)=a(x-m)^2+n$.
According to the picture the vertex of the graph is at $(-2,6)$, hence the quardatic function becomes $f(x)=a(x+2)^2+6$.
The point $(-4,-2)$ is on the graph, hence if we plug in the values we get:
$-2=a(-4+2)^2+6\\-2=a(4)+6\\-8=4a\\a=-2$
Thus, the equation of the function is $f(x)=-2(x+2)^2+6$.
