Answer
$f(x)=-(x-2)^2+3$
Work Step by Step
If the vertex of a graph is at $(m,n)$ then the vertec form for the quadratic function is $f(x)=a(x-m)^2+n$.
According to the picture the vertex of the graph is at $(2,3)$, hence the quadratic function becomes $f(x)=a(x-2)^2+3$.
The point $(0,-1)$ is on the graph, hence if we plug in the values we get:
$-1=a(0-2)^2+3
\\-1=4(a)+3\\
-4=4a
\\a=-1$
Thus, the equation of the function is $f(x)=-(x-2)^2+3$.
