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 32 feet per second from a platform that is 23 feet high. The height of the arrow is given by the function $h ( t ) = - 16 t ^ { 2 } + 32 t + 23$, where $t$ is the time is seconds. What is the maximum height of the arrow?
A) $16 \mathrm { ft }$
B) $23 \mathrm { ft }$
C) $22 \mathrm { ft }$
D) $39 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The maximum height of the arrow corresponds to the vertex of the parabola described by the function $h(t) = -16t^2 + 32t + 23$. 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 $b = 32$. Thus, $t = -\frac{32}{2(-16)} = 1$. Substituting $t = 1$ back into the function gives the maximum height: $h(1) = -16(1)^2 + 32(1) + 23 = -16 + 32 + 23 = 39$ feet.

Find the Vertex, the Y-Intercept, and the X-Intercepts (If Any h(t)=−16t2+32t+23h ( t ) = - 16 t ^ { 2 } + 32 t + 23h(t)=−16t2+32t+23

Find the Vertex, the Y-Intercept, and the X-Intercepts (If Any $h ( t ) = - 16 t ^ { 2 } + 32 t + 23$