If an object is thrown upward with an initial velocity of $12 \mathrm{ft}$ per sec, then its height (in feet) is given by $h(t)=-12 t^{2}+72 t$ after time $t$ seconds. What is its maximum height?
A) $36 \mathrm{ft}$
B) $108 \mathrm{ft}$
C) $147 \mathrm{ft}$
D) $144 \mathrm{ft}$

Question

Quizplus · Accepted Answer

The maximum height can be found by completing the square or using the vertex formula for a parabola. The given equation is in the form $h(t) = -12t^2 + 72t$. The vertex of a parabola given by $y = ax^2 + bx + c$ is at $(-b/2a, h(-b/2a))$. Here, $a = -12$ and $b = 72$, so the time at which the maximum height is reached is $-72/(2 \cdot -12) = 3$ seconds. Plugging $t = 3$ back into the equation gives the maximum height: $h(3) = -12(3)^2 + 72(3) = -108 + 216 = 108$ 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 $12 \mathrm{ft}$