Answer:
The correct option is C.
Step-by-step explanation:
The height of the ball is defined by a parabolic function.
Let the equation of the parabola is
[tex]f(x)=a(x-h)^2+k[/tex]
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
[tex]f(x)=a(x-2.2)^2+15[/tex]
The initial height of the ball is 0.
[tex]f(0)=a(0-2.2)^2+15[/tex]
[tex]0=a(-2.2)^2+15[/tex]
[tex]a=-\frac{15}{(2.2)^2}[/tex]
[tex]a=-3.1[/tex]
The equation of the parabola is
[tex]f(x)=-3.1(x-2.2)^2+15[/tex]
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.
[tex]2.2+2.2=4.4[/tex]
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
[tex]0\leq x\leq 4.4[/tex]
Therefore option C is correct.
