Answer
$f(x)=-3(x+1)^2+12$
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 $(k,k) =(-1,12)$, therefore we have $$h=-1,\quad k=12.$$. We know that: $$f(x) = a(x-h)^2+k $$ Hence, we can write, using the values of $h$ and $k$: \begin{equation}
\begin{aligned}
f(x)=a(x+1)^2+12.
\end{aligned}
\end{equation} We also see that when $x=1 $, $y= 0$. Using the point $(1,0)$, which means that $f(1)=0$, we determine $a$:
\begin{equation}
\begin{array}{r}
a(1+1)^2+12=0 \\
4a+12=0\\
4a=-12\\
a=-\frac{12}{4}= -3.
\end{array}
\end{equation}
The solution is: $$f(x)=-3(x+1)^2+12.$$
