Answer
$f(x)=-2(x+2)^2+6$.
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 (-2,6), hence the quadratic 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 $-2=4a+6$, hence a=-2, hence $f(x)=-2(x+2)^2+6$.
