Question

Suppose the function, g(x), is used to model the height ,y, of a soccer ball, x seconds after the ball is kicked up in the air. The ball starts on the ground and travels in a parabolic shape as it reaches a maximum height and then returns to the ground. Suppose further that the ball reaches its maximum height of 15 feet in 2.2 seconds. What would be an appropriate domain for g(x)?

A. 0<=x<=2.2
B. -2.2<=x<=2.2
C. 0<=x<=4.4
D. 0<=x<=15

Answer 1

The correct option is C.

Explanation:

The height of the ball is defined by a parabolic function.

Let the equation of the parabola is

`f(x)=a(x-h)^2+k`

Where, (h,k) is the vertex and a is stretch factor.

The maximum height of the ball is 15 feet in 2.2 seconds. So, the vertex is (2.2, 15).

The equation of the parabola is

`f(x)=a(x-2.2)^2+15`

The initial height of the ball is 0.

`f(0)=a(0-2.2)^2+15`

`0=a(-2.2)^2+15`

`a=-(15)/((2.2)^2)`

`a=-3.1`

The equation of the parabola is

`f(x)=-3.1(x-2.2)^2+15`

The function takes 2.2 seconds to reach at maximum height, so after that it will take 2.2 seconds to reach at growth again.

`2.2+2.2=4.4`

The ball will reach the growth at x=4.4.

The height can not be negative, therefore the value of x lies between 0 to 4.4. The domain of the function is

`0\leq x\leq 4.4`

Therefore option C is correct.