Algebra word problem (quadratic formula)

Question

A model rocket is launched straight upward from the side of a 212-ft cliff. The initial velocity is 86 ft/sec. The height of the rocket h(t) is given by:

 

h(t)=-16t²+86t+212

 

where h(t) is measured in feet and t is the time in seconds. Use the quadratic formula to find the times (t) at which the rocket is 300 ft. above the ground. Round your answers to the nearest hundredth of a second.

This is a 10-point question so make sure you are showing ALL steps. You will not be granted a redo if your work is lacking.

Answer 1

When is h(t) = 300

-16t² + 86t + 212 = 300

16t² - 86t - 88 = 0

2(8t² - 43t - 44) = 0

8t² - 43t - 44 = 0

 

In the above quadratic equation, a = 8, b = -43, and c = -44. Plug those values into The Quadratic Formula to find the value for t such that the rocket is 300 ft above the ground. Remember that t is a unit of time, so it cannot be negative. You will obtain two roots when using The Quadratic Formula. You will need to select the positive root.