Answer
$f(x)=-(x+3)^2+5$
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 $(-3,5)$, hence the quadratic function becomes $f(x)=a(x+3)^2+5$.
The point $(0,-4)$ is on the graph, hence if we plug in the values we get
$-4=a(0+3)^2+5\\-9=a(9)\\-1=a.$
Thus, the equation of the function is $f(x)=-(x+3)^2+5$.
