Answer
$68$ ft
Work Step by Step
$h(t)=-16t^2+48t+32$,
To find the maximum height, we can turn an equation from a standard form into a vertex form by completing the square.
$h(t)=-16(t^2-3t)+32$,
$h(t)=-16\left(t^2-3t+\frac{9}{4}\right)+32+36$, $h(t)=-16\left(t-\frac{3}{2}\right)^2+68$,
Therefore, we can see that from an equation the maximum height is $68$ ft as $\left(\frac{3}{2},68\right)$ is the vertex and because the leading coefficient is negative, the vertex in the point where the function reaches its maximum.
