Question

write a quadratic function to model the vertical motion for each situat initial vertical velocity: 64 ft/s; initial height: 80 ft the function is h(t) = -16t² + 64t + 80. the maximum height is

Explanation:

Step1: Find time of max height

For quadratic $h(t)=at^2+bt+c$, time $t=-\frac{b}{2a}$.
Here $a=-16$, $b=64$, so $t=-\frac{64}{2(-16)} = 2$ seconds.

Step2: Substitute t into h(t)

Calculate $h(2)=-16(2)^2+64(2)+80$.
$h(2)=-16(4)+128+80=-64+128+80=144$

Answer:

144 ft