The expression LaTeX: - 5t^2+40t

-

5

t

2

+

40

t

predicts the height, in meters of an object t seconds after a person launches it into the air.

It will take _ seconds for the object to hit the ground.

8 seconds

Step-by-step explanation:

Given

h = - 5t² + 40t

When the object hits the ground then h = 0

Substitute h = 0 into the function and solve for t

- 5t² + 40t = 0 ← factor out - 5t from each term

- 5t (t - 8) = 0

Equate each factor to zero and solve for t

- 5t = 0 ⇒ t = 0

t - 8 = 0 ⇒ t = 8

t = 0 denotes the time of launch

t = 8 denotes the time it hits the ground