Answer
See graph
Work Step by Step
Using the vertex $(h,k)=(7,9)$, we write $$f(x)=a(x-7)^2+9.$$ To determine $a$ use the vertical intercept: $$\begin{aligned}
f(0) &= 58\\
a(0-7)^2+ 9&=58\\
49a& =49\\
a&=1.
\end{aligned}$$ The function is completely determined: $$f(x)=(x-7)^2+9.$$ The graph of the function is shown below with the vertex at $ (7,9)$, vertical intercept at $(0,58)$ and an additional point of symmetry.
