I am wondering if my answers to these two questions are actually correct. If they are not correct, then I'm looking to see if someone can show the work on how to get the answer to these homework review questions. For question $1$, the answer for the max height I got was $64$. For question $2$, the answer for the time it takes for the ball to reach the ground was $3$ seconds. I used the quadratic formula for question 2 after simplifying the equation and received $3$ seconds as my answer. Are these answers to my homework questions correct?
The height of a ball thrown straight up from a building is given by $h(t)=-16t^2+32t+48$, $t$ seconds after it is thrown.
$1)$ Find the maximum height of the ball.
$2)$ Find the time it takes for the ball to reach the ground.
Best Answer
$1)$ $h(t) = -16(t-1)^2+64 \le 64$ and the max height is $64$. For $2)$, $h(t) = 0 \implies (t-1)^2 = 4 \implies t-1 = 2 \implies t = 3$. So yes, you got it right.