Answer
The vertex is $(-2.25,-\pi)$
The axis of symmetry is $x=-2.25.$
The maximum function value is $-\pi.$
Work Step by Step
$ f(x)=-\sqrt{2}(x+2.25)^{2}-\pi$
$a=-\sqrt{2}$
$h=-2.25$
$ k=-\pi$
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 $(-2.25,-\pi)$
The axis of symmetry is $x=-2.25.$
Since $a\lt 0$, the maximum function value is $-\pi.$