Question

Benjamin kicks a ball off the ground, and the ball travels at an initial velocity of 48 feet per second. An equation is used to model the height, in feet, of the ball from the time it is kicked to the time it returns to the ground. The height, h (t), in feet, of the ball t seconds after it is kicked is represented by the function shown. h (t) 16t + 48t Select all the values ​​that are included in the domain of h (t)

Answer 1

Explanation:

The domain of h(t) is the set of all input values (in this case, the time t) that make the function h(t) produce a real output.

In this case, the equation used is h(t) = -16t^2 + 48t + 48, this equation describes the height of the ball at different times, where the variable t is the time in seconds after the ball is kicked.

For the function to produce a real output, the value of t must be such that the value inside the square root is greater than or equal to zero, and the denominator is not zero. So, h(t) = -16t^2 + 48t + 48, is defined for all real numbers t > 0 .

Therefore, the domain of h(t) would be all values of t that are greater than 0.

Answer 2

0, 1.5, and 3

Explanation:

Solve h(t) = -16t² + 48t

0 = -16t² + 48t set it equal to zero because we want to know how long it takes the ball to return to the ground. That gives us the domain of the function.

0 = t² - 3t (divide both sides by -16)

0 = t(t - 3) (factor out a t)

So

t = 0

or

t - 3 = 0

t = 3

So the ball leaves the ground at zero seconds and returns to the ground at 3 seconds. The domain of the function is all values from 0 to 3