Question

The quadratic model f(x)=-5x^2 +200 represents the approximate height, in meters, of a ball x seconds after being dropped. The ball is 50 meters from the ground after about how many seconds

2.45
3.16
5.48
7.07

Answer 1

5.48

Explanation:

Answer 2

Third option: 5.48

Explanation:

Given the quadratic model that represents the approximate height in meters of the ball
`f(x)=-5x^2 +200`. the time in seconds x, when the ball is 50 meters from the ground can be calculated by substituting
`f(x)=50` and solving for x.

Then:

`50=-5x^2 +200`

Subtract 200 from both sides:

`-200+50=-5x^2 +200-200\\-150=-5x^2`

Divide both sides by -5:

`(-150)/(-5)=(-5x^2)/(-5)\\30=x^2`

Apply square root to both sides:

`√(30)=√(x^2)\\√(30)=x\\5.48=x`

The ball is 50 meters from the ground after about 5.48 seconds.