how to determine which formula should be used to solve this problem

Question

if an object is propelled upward from a height of 48 feet at a initial velocity of 96 feet per second, then its height after t seconds is given by the equation h(t) = -16t^2 + 96t + 48, where height is in feet. after how many seconds will the object reach a height of 192 feet?

Answer 1

h(t) gives the height after t seconds

if we set the equation equal to 192 then we can solve for t

192 = -16t² + 96t + 48

0 = -16t² + 96t - 144

0 = -16(t² - 6t + 9)

0 = -16(t - 3)(t - 3)

then t = 3 seconds is the time it takes for the object to reach a height of 192 feet