Question

show what you know: quadratic applications
possible points: 3.33
a toy rocket is fired into the air from the top of a barn. its height $h$ above the ground in yards after $t$ seconds is given by the function
$h(t)=-5t^{2}+10t+20$. the initial height of the rocket is $\boldsymbol{square}$ feet above the ground. the rocket reached its maximum height after $\boldsymbol{square}$ second(s).

Explanation:

Step1: Find initial height (t=0)

Substitute $t=0$ into $h(t)$:
$h(0) = -5(0)^2 + 10(0) + 20 = 20$
Note: The function uses yards, convert to feet: $20 \times 3 = 60$

Step2: Find time for max height

For quadratic $at^2+bt+c$, time is $t=-\frac{b}{2a}$:
$t = -\frac{10}{2(-5)} = \frac{-10}{-10} = 1$

Answer:

The initial height of the rocket is 60 feet above the ground. The rocket reached its maximum height after 1 second(s).