Question

Antoine stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), x seconds after Antoine threw it, is modeled by: h(x)=-2x^2+4x+16. How many seconds after being thrown will the ball hit the ground?

Answer 1

4 seconds

Explanation:

Given : The ball's height (in meters above the ground), x seconds after Antoine threw it, is modeled by:
`h(x)=-2x^2+4x+16.`

To Find: How many seconds after being thrown will the ball hit the ground?

Solution:

We are supposed to find after how much time the ball hits the ground.

So, we are required to substitute h = 0 because when ball hits the ground the height will be 0

So,
`0=-2x^2+4x+16`

`2x^2-4x-16=0`

`x^2-2x-8=0`

`x^2-4x+2x-8=0`

`x(x-4)+2(x-4)=0`

`(x-4)(x+2)=0`

`x=4,-2`

Since time cannot be negative .So, neglect -2

Hence A ball will take 4 seconds to hit the ground after being thrown.

Answer 2

Explanation:

H(x)=0

-2x^2 +4x+16=0

X^2 - 2x - 8 = 0

(X + 2) (x-4) = 0

X + 2 = 0 or x -4 = 0

X= -2 or x=4

Since -2 doesn’t make sense use 4

The ball will hit ground in 4 seconds