Answer
1. At $2$ seconds the baseball reaches its maximum height.
2. $69$ feet is the maximum height the baseball reaches.
Work Step by Step
$s(t) = -16t^{2} + 64t + 5$
1. Use the axis of symmetry to find the $x$ coordinate of the vertex
$= -\frac{b}{2a}$
$= -\frac{64}{2(-16)}$
$= - \frac{64}{-32}$
$t = 2$
At $2$ seconds the baseball reaches its maximum height.
2. Use the axis of symmetry to find the $y$ coordinate of the vertex
$s(2) = -16(2)^{2} + 64(2) + 5$
$= -16(4) + 128 + 5$
$= -64 + 133$
$= 69$
$69$ feet is the maximum height the baseball reaches.
