Answer
$f(x) =(x+1)^2-9 $
Work Step by Step
An equation of the function can be found by first finding the vertex and another point on the graph. From the graph we see that the vertex of the function is $(h,k) =(-1,-9)$, therefore we have: $$h=-1,\quad k=-9.$$. We know that:
$$f(x) = a(x-h)^2+k. $$ Hence, replacing $h$ and $k$, we can write:
\begin{equation}
\begin{aligned}
f(x) & =a(x+1)^2-9.
\end{aligned}
\end{equation} We also see that when $x=2 $, $y= 0$. Using the point $(2,0)$, we determine $a$ because $f(2)=0$: \begin{equation}
\begin{array}{r}
a(2+1)^2-9=0 \\
9a-9=0\\
9a=9 \\
a=1.
\end{array}
\end{equation} The solution is: $$f(x) =(x+1)^2-9 .$$
