Answer:
See attachment.
Explanation:
The quadratic function f(t) models the height of the ball, in feet, as a function of the time t in seconds, from the time it is thrown to the time it hits the ground.
Initial Position: y-intercept
The ball is thrown upward from a cliff 48 feet above the ground. This means that at t = 0, the initial height is 48 feet. So, the y-intercept of the graphed function is (0, 48).
Maximum Height: vertex
The ball rises to a maximum height of 64 feet. This represents the vertex of the parabolic graph. So the maximum y-value of the graphed function is y = 64.
Time of Flight: domain
The ball hits the ground 3 seconds after it is thrown. This means that the height of the ball is zero at t = 3, and therefore the x-intercept is (3, 0). So the domain of the function is [0, 3].
Considering these details, the graph that represents the function is the top right graph because it has:
- A y-intercept at (0, 48).
- A maximum y-value at y = 64.
- An x-intercept at (3, 0).