Find the vertex, the y-intercept, and the x-intercepts (if any exist), and graph the function.
-April shoots an arrow upward into the air at a speed of 64 feet per second from a platform that is 35 feet high. The height of the arrow is given by the function $h ( t ) = - 16 t ^ { 2 } + 64 t + 35$, where $t$ is the time is seconds. What is the maximum height of the arrow?
A) $99 \mathrm { ft }$
B) $64 \mathrm { ft }$
C) $31 \mathrm { ft }$
D) $35 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The maximum height of the arrow corresponds to the vertex of the parabola described by the function $h(t) = -16t^2 + 64t + 35$. The vertex can be found using the formula $t = -\frac{b}{2a}$ for the time at which the maximum height occurs, where $a = -16$ and $b = 64$. Substituting these values gives $t = -\frac{64}{2(-16)} = 2$. Plugging $t = 2$ back into the function gives the maximum height: $h(2) = -16(2)^2 + 64(2) + 35 = -64 + 128 + 35 = 99$ ft.

Find the Vertex, the Y-Intercept, and the X-Intercepts (If Any h(t)=−16t2+64t+35h ( t ) = - 16 t ^ { 2 } + 64 t + 35h(t)=−16t2+64t+35

Find the Vertex, the Y-Intercept, and the X-Intercepts (If Any $h ( t ) = - 16 t ^ { 2 } + 64 t + 35$