Question

the height h(t) of a rocket is modeled by h(t) = -5t² + 30t + 10. what is the maximum height the rocket will reach? a. 50 meters b. 40 meters c. 55 meters d. 60 meters

Explanation:

Step1: Find time at max height

For quadratic $h(t)=at^2+bt+c$, max at $t=-\frac{b}{2a}$. Here $a=-5$, $b=30$.
$t=-\frac{30}{2(-5)}=3$

Step2: Calculate max height

Substitute $t=3$ into $h(t)$:
$h(3)=-5(3)^2 + 30(3) + 10=-45+90+10=55$

Answer:

c. 55 meters