A projectile is thrown upward so that its distance (in feet) above the ground after $t$ seconds is given by $h(t)=-14 t^{2}+616 t$. What is its maximum height?
A) $24,200 \mathrm{ft}$
B) $347,424 \mathrm{ft}$
C) $6776 \mathrm{ft}$
D) $8428 \mathrm{ft}$

Question

Quizplus · Accepted Answer

The maximum height of a projectile in the form $h(t) = -at^2 + bt + c$ can be found using the vertex formula for a parabola, $t = -\frac{b}{2a}$. Here, $a = -14$ and $b = 616$, so $t = -\frac{616}{2(-14)} = 22$. Plugging this back into the equation for $h$, $h(22) = -14(22)^2 + 616(22) = 6776$ feet.

A Projectile Is Thrown Upward So That Its Distance (In ttt

A Projectile Is Thrown Upward So That Its Distance (In $t$