Answer
144 feet
Work Step by Step
$h(t)=-16t^2+96t$
Since the graph opens downward, the vertex will have the highest point on the graph.
$a=-16$, $b=96$, $c=0$
Vertex: $x=-b/2a$
$x=-96/2*-16$
$x=-96/-32$
$x=3$
$h(t)=-16t^2+96t$
$h(3)=-16(3)^2+96(3)$
$h(3)=-16*9+288$
$h(3)=-144+288$
$h(3)=144$ feet
144 feet