Answer
The maximum height is 272 feet.
Work Step by Step
We know the location of the vertex is $-\frac{b}{2a}$. Thus:
$$ t_{critical}=-\frac{32}{(-16)(1)}\\ t_{critical}=1\ s$$
The maximum occurs at 1 second. Thus, we plug 1 second into the original function:
$$ s(1) = (-16)(1^2) + 32(1) + 256 \\ = 272\ ft$$
