Answer
$21$
Work Step by Step
We are given $$h(z)=-2 z^{2}+12 z+3$$
We factor the equation to get it into parabola/quadratic form:
\begin{align*}
h(z)&=-2 z^{2}+12 z+3\\
&= -2[z^2-6z-3/2]\\
&= -2[(z-3)^2-9-3/2] \\
&=-2(z-3)^{2}+21
\end{align*}
Compare with the quadratic function
$$f(x)=a(x-h)^{2}+k$$
We see that the vertex is $(h,k)= (3,21)$. Since $a<0$, then the maximum value is $f(3)=21$
