Answer
16 feet
Work Step by Step
$h(t)=-16t^2+32t$
Since the graph opens downward, the vertex will have the highest point on the graph.
$h(t)=-16t^2+32t$
$a=-16$, $b=32$, $c=0$
Vertex: $x=-b/2a$
$x=-(32)/2*(-16)$
$x=-32/-32$
$x=1$
$h(t)=-16t^2+32t$
$h(1)=-16*1^2+32*1$
$h(1)=-16*1+32$
$h(1)=-16+32$
$h(1)=16$
16 feet