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