Answer
$2$ seconds
$69$ feet
Work Step by Step
The quadratic function
$$s(t)=-16t^2+64t+5$$
has negative leading coefficient, therefore its graph is a parabola that opens downward and has a maximum in the vertex.
Bring the function to the vertex form $f(x)=a(x-h)^2+k$:
$$\begin{align*}
s(t)&=-16t^2+64t+5\\
&=-16(t^2-4t)+5\\
&=-16(t^2-4t+4)+16(4)+5\\
&=-16(t-2)^2+69.
\end{align*}$$
Identify the constants $a$, $h$, $k$:
$$\begin{align*}
a&=-16\\
h&=2\\
k&=69.
\end{align*}$$
Determine the vertex of the function:
$$(h,k)=(2,69).$$
So the amount of time until the ball reaches its maximum height is $2$ seconds, while the maximum height is $69$ feet.
