Solve the problem.
-April shoots an arrow upward into the air at a speed of 64 feet per second from a platform that is 22 feet high. The height of the arrow is given by the function $h ( t ) = - 16 t ^ { 2 } + 64 t + 22$, where $t$ is the time is seconds. What is the maximum height of the arrow?
A) $86 \mathrm { ft }$
B) $18 \mathrm { ft }$
C) $64 \mathrm { ft }$
D) $22 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The maximum height of the arrow can be found by using the vertex formula for a quadratic equation $h(t) = -16t^2 + 64t + 22$. The vertex formula $t = -\frac{b}{2a}$ gives the time at which the maximum height is reached. Here, $a = -16$ and $b = 64$, so $t = -\frac{64}{2(-16)} = 2$. Substituting $t = 2$ back into the equation gives the maximum height: $h(2) = -16(2)^2 + 64(2) + 22 = 86$ feet.

Solve the Problem h(t)=−16t2+64t+22h ( t ) = - 16 t ^ { 2 } + 64 t + 22h(t)=−16t2+64t+22

Solve the Problem $h ( t ) = - 16 t ^ { 2 } + 64 t + 22$