If an object is thrown upward with an initial velocity of $12 \mathrm{ft}$ per sec, then its height (in feet) is given by $h(t)=-12 t^{2}+48 t$ after time $t$ seconds. What is its maximum height?
A) $24 \mathrm{ft}$
B) $144 \mathrm{ft}$
C) $48 \mathrm{ft}$
D) $146 \mathrm{ft}$

Question

Quizplus · Accepted Answer

The maximum height is found by determining the vertex of the parabola described by the quadratic equation $h(t)=-12t^2+48t$. The vertex occurs at $t = -\frac{b}{2a} = -\frac{48}{2(-12)} = 2$. Substituting $t = 2$ into the equation gives $h(2) = -12(2)^2 + 48(2) = 48$ feet.

If an Object Is Thrown Upward with an Initial Velocity 12ft12 \mathrm{ft}12ft

If an Object Is Thrown Upward with an Initial Velocity $12 \mathrm{ft}$