Answer
$y=-2x^2+12x-10$
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 at $(3, 8)$ so we have $h=3$ and $k=8$.
Thus, the equation of the function whose graph is given is: $$y=a(x-3)^2+8$$
Since the graph contains the point $(1, 0)$, substitute the $1$ to $x$ and $0$ to $y$ to obtain:
\begin{align*}
0&=a(1-3)^2+8\\
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:
$$y=-2(x-3)^2+8$$
Expand the binomial then simplify to obtain:
\begin{align*}
y&=-2(x^2-6x+9)+8\\
y&=-2x^2+12x-18+8\\
y&=-2x^2+12x-10
\end{align*}
