It's a parabola with zeros at x=-4 and x=0 and we know f(-2)=4 is the vertex.
The concave downward orientation means it has a minus sign on the quadratic term.
Vertex form suggests
f(x) = -(x + 2)² + 4
We check f(0)=-4+2=0 and f(-4)=-(-4 + 2)² + 4 = -4 + 4 = 0, good
Answer: first choice