Answer
272 feet
Work Step by Step
$s(t)=-16t^2+32t+256$
The maximum height is the $y$ value of the vertex. The vertex is on the axis of symmetry.
The vertex is on the axis of symmetry, $x=-b/2a$
$x=-b/2a$
$a=-16$, $b=32$, $c=256$
$x=-b/2a$
$x=-32/2*-16$
$x=-32/-32$
$x=1$
$s(t)=-16t^2+32t+256$
$s(1)=-16*1^2+32*1+256$
$s(1)=-16*1+32+256$
$s(1)=-16+32+256$
$s(1)=16+256$
$s(1)=272$
