A model rocket is launched from a raised platform at a speed of 112 feet per second. Its height in feet is given by $h ( t ) = - 16 t ^ { 2 } + 112 t + 20$ (t = seconds after launch) What is the maximum height reached by the rocket?
A) 216 feet
B) 432 feet
C) 108 feet
D) 236 feet

Question

Quizplus · Accepted Answer

The maximum height of the rocket can be found by using the vertex formula for a quadratic equation $h(t) = -16t^2 + 112t + 20$. The t-coordinate of the vertex is given by $-\frac{b}{2a}$, where $a = -16$ and $b = 112$. Thus, $t = -\frac{112}{2(-16)} = 3.5$. Plugging this back into the equation for $h(t)$ gives the maximum height: $h(3.5) = -16(3.5)^2 + 112(3.5) + 20 = 216$ feet.

A Model Rocket Is Launched from a Raised Platform at a Speed