Answer
$
y=-\frac{1}{4}\cdot(x+7)^2-3
$
Work Step by Step
We have $(h, k)=(-7,-3)$, so $y=a(x+7)^2-3$. Solve for $a$ using point, $x= -3$ and $y= -7$.
$$
\begin{aligned}
a(-3+7)^2-3 & =-7 \\
16 a & =-4 \\
a & =-\frac{1}{4}
\end{aligned}
$$ Hence
$$
y=-\frac{1}{4}\cdot(x+7)^2-3
$$
