Question

The height of an object seconds after it is launched is modeled by the function h(t)=-4t^2+16t+180. When will the object hit the ground?

Answer 1

9 seconds after the object is launched

Explanation:

The function models the height of the object as a function of the time after the object is launched. Therefore h(t) will be zero, and you will solve for t like a normal quadratic equation.

0 = -4t² + 16t + 180

First, you can factor out the -4 from all the terms.

0 = -4(t² - 4t - 45)

Next, factor what is inside the parentheses

0 = -4 (t + 5) (t - 9)

Then you set each of the factors individually to zero and solve

t + 5 = 0 and t - 9 =0

From this we get that time is:

t = -5 and t = 9

Now that time cannot be negative, we figure out that the time is 9 seconds, therefore the object will hit the ground after 9 seconds.