Question

The function f(t) = −5t 2 + 20t + 60 models the approximate height of an object

t seconds after it is launched. How many seconds does it take the object to hit the
ground?

Answer 1

f(t) = -5t^2 + 20t + 60
-5(t^2 - 4t - 12)
-5(t + 2) (t - 6)
t = -2 or t = 6

6 seconds

Answer 2

6 seconds.

Explanation:

We have been given a function formula
`f(t)=-5t^2+20t+60` that models the approximate height of an object t seconds after it is launched.

To find the number of seconds it will take the object to hit the ground, we need to find the zeros of our given function.

`-5t^2+20t+60=0`

Upon dividing our equation by -5 we will get,

`t^2-4t-12=0`

We will factor our given equation by splitting the middle term as:

`t^2-6t+2t-12=0`

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

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

`(t-6)=0\text{ or }(t+2)=0`

`t=6\text{ or }t=-2`

Since time cannot be negative, therefore, it will take the object 6 seconds to hit the ground.