Maths word problem with equation

Question

A Tennis ball is thrown into Swimming pool from the top of a tall hotel. The height of the ball from the pool is modeled by

D(t) = -16t2-4t +300 feet, where t is the time, in seconds, after the ball was thrown. How long after the ball was thrown was it 144 feet above the pool?

Answer 1

The question asks for time given distance. Simply plug in 144 feet for D(t) and solve for t:

144 = -16t² - 4t + 300

Subtract 144 from both sides:

-16t² - 4t + 300 - 144 = 0

-16t² - 4t + 156 = 0

Divide the whole equation by -4 to simplify:

4t² + t - 39 = 0

Use the quadratic formula to solve:

x = [-1 +_- sqrt(1² - 4(4)(-39))] / [2(4)]

x = (-1 +_- 25)/8

x = 24/8 or -26/8

x = 3 or a negative number

Time can't be negative in this scenario so the answer is 3 seconds