Answer
The vertex is $(3,9)$
The axis of symmetry is $x=3.$
The minimum function value is $9$.
Work Step by Step
$f(x)=5(x-3)^{2}+9$
$a=5$
$h=3$
$k=9$
The vertex is $(h, k)$, and the axis of symmetry is $x=h.$
For $a\gt 0$, the minimum function value is $k$.
For $a\lt 0$, the maximum function value is $k.$
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The vertex is $(3,9)$
The axis of symmetry is $x=3.$
Since $a\gt 0$, the minimum function value is $9$.