Suppose a ball is thrown into the air and after t seconds has a height of $h ( t ) = - 16 t ^ { 2 } + 80 t$ feet. When will it reach its maximum height?
A) 5 sec
B) 300 sec
C) 0.5 sec
D) 2.5 sec
E) none of these

Question

Quizplus · Accepted Answer

The function $h(t) = -16t^2 + 80t$ is a quadratic equation in the form $at^2 + bt + c$. The maximum height is reached at the vertex of the parabola, which occurs at $t = -\frac{b}{2a}$. Here, $a = -16$ and $b = 80$, so $t = -\frac{80}{2(-16)} = 2.5$ seconds.

Suppose a Ball Is Thrown into the Air and After h(t)=−16t2+80th ( t ) = - 16 t ^ { 2 } + 80 th(t)=−16t2+80t

Suppose a Ball Is Thrown into the Air and After $h ( t ) = - 16 t ^ { 2 } + 80 t$