Answer
$f(x)=-2(x+2)^2+6$
Work Step by Step
The vertex form of the quadratic function $ax^2+bx+c=0$ can be expressed as $f(x)=a(x-h)^2+k$ and its vertex is at $(h, k)$.
As depicted in the picture, the vertex of the graph is at $(h, k)=(-2,6)$, and thus, the vertex form for the quadratic function becomes $f(x)=a(x+2)^2+6$.
Plug in the values $(-4, -2)$ to obtain:
$-2=a(-4+2)^2 +6 \\ 4a=-8 \implies a=-2$
Therefore, the equation of the function can be expressed as: $f(x)=-2(x+2)^2+6$
