Solve for how much seconds for the object to hit the ground

Question

If the function f(t)=-5t²⁺20t+60 models the approximate height of an an object after it is launched then how many seconds does it take the object to hit the ground?

Answer 1

You can also write this function in vertex form.

 

f(t) = -5t² + 20t + 60

 

f(t) = -5(t² - 4t + 4) + 20 + 60

 

f(t) = -5(t - 2)² + 80

 

 

The time it reaches its maximum height is 2 seconds.

Answer 2

f(t) = -5t² + 20t + 60

 

Set f(t)=0 and solve for t.

 

-5t² + 20t + 60 = 0

t² - 4t - 12 = 0

(t - 6)(t + 2) = 0

 

Time is positive, so

 

t = 6 seconds.