Answer
$y=-2x^2+8$
Work Step by Step
Recall:
The equation of a quadratic function whose vertex is at $(h, k)$ is given by the equation $y=a(x-h)^2+k$
The graph shows that vertex of the function is at $(0, 8)$ so we have $h=0$ and $k=8$.
Thus, the equation of the function whose graph is given is: $$y=a(x-0)^2+8\longrightarrow y=ax^2+8$$
Since the graph contains the point $(2, 0)$, substitute the $2$ to $x$ and $0$ to $y$ to obtain:
\begin{align*}
0&=a(2)^2+8\\
0&=a(4)+8\\
-8&=4a\\
-2&=a
\end{align*}
Therefore, the equation of the quadratic function whose gaph is given is:
$$y=-2x^2+8$$