Story problem for algebra 2

Question

A ball is thrown into the air where it’s height in feet (h) and time in seconds (t) can be found by the following equation,  h = -16t² + 48t +288. Find the maximum height of the ball and how long it takes for the ball to hit the ground.

Answer 1

h' = -32t + 48 = 0 for maximum height time

t= 48/32 = 3/2 = 1.5 seconds at max height

max h = -16(1.5)^2 + 48(1.5) + 288 = -16(2.25) + 72 + 288 =-36 + 360 = 324 feet

it hits the ground when h=0 = -16t^2 + 48t + 288

divide by -16

t^2 -3t - 8 = 0

use the quadratic formula

t-3t + 9/4 = 8 + 9/4

(t-3/2)^2 = 41/4

t-3/2 = sqr(41/4)

t = 3/2 + (1/2)sqr41 = 1.5 + .5(6.403) = 1.5 + 3.2 = 4.5 seconds when it hits the ground