Question

write a quadratic function to model the vertical motion for each situation, given $h(t) = -16t^2 + v_0t + h_0$. find the maximum height. initial vertical velocity 64 ft/s, initial height 80 ft the function is $h(t) = \square$

Explanation:

Step1: Substitute initial values

Substitute $v_0=64$, $h_0=80$ into $h(t)=-16t^2+v_0t+h_0$:
$h(t) = -16t^2 + 64t + 80$

Step2: Find vertex t-value

For $ax^2+bx+c$, vertex $t=-\frac{b}{2a}$:
$t = -\frac{64}{2\times(-16)} = 2$

Step3: Calculate max height

Substitute $t=2$ into $h(t)$:
$h(2) = -16(2)^2 + 64(2) + 80 = -64 + 128 + 80 = 144$

Answer:

The function is $h(t) = -16t^2 + 64t + 80$, and the maximum height is 144 ft.