Answer
The vertex is $(-8,2)$
The axis of symmetry is $x=-8.$
The maximum function value is $2$.
Work Step by Step
$f(x)=-\displaystyle \frac{3}{7}(x+8)^{2}+2$
$a=-\displaystyle \frac{3}{7}$
$h=-8$
$k=2$
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 $(-8,2)$
The axis of symmetry is $x=-8.$
Since $a\lt 0$, the maximum function value is $2.$