Answer
$y=\frac{10}{9}(x+2)^2+5$
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 $(-2, 5)$ so we have $h=-2$ and $k=5$.
Thus, the equation of the function whose graph is given is: $$y=a[x-(-2)]^2+5\longrightarrow y=a(x+2)^2+5$$
Since the graph contains the point $(1, 15)$, substitute the $1$ to $x$ and $15$ to $y$ to obtain:
\begin{align*}
15&=a(1+2)^2+5\\
15&=a(3)^2+5\\
15-5&=a(9)\\
10&=9a\\
\frac{10}{9}&=a
\end{align*}
Therefore, the equation of the quadratic function whose gaph is given is:
$$y=\frac{10}{9}(x+2)^2+5$$
