Answer
$f(x)=(x+1)^2-2$.
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 $(h, k)=(-1,-2)$, and thus, the quadratic function becomes $f(x)=a(x+1)^2-2$.
Plug in the values $(0,-1)$ to obtain:
$-1=a(0+1)^2-2 \implies a=1$
Therefore, the equation of the function can be expressed as:
$f(x)=(x+1)^2-2$.
