Use the image to answer the question.

Question

A curve is plotted in the first quadrant of a coordinate plane. The x-axis for Time in seconds ranges from 0 to 1.25 in increments of 0.25 and the y-axis for Height in feet ranges from 0 to 18 in increments of 2.

The graph here represents the height of a ball when being dropped from a height of 16 feet. Which of the following points can be used to find the quadratic equation that models the graph?

(1 point)
Responses

(16,0)
, (12,0.5)
, and (0,1)
left parenthesis 16 comma 0 right parenthesis , left parenthesis 12 comma 0.5 right parenthesis , and left parenthesis 0 comma 1 right parenthesis

(0,16)
, (0.5,12)
, and (1,0)
left parenthesis 0 comma 16 right parenthesis , left parenthesis 0.5 comma 12 right parenthesis , and left parenthesis 1 comma 0 right parenthesis

(0,16)
, (0.375,14)
, and (1,0)
left parenthesis 0 comma 16 right parenthesis , left parenthesis 0.375 comma 14 right parenthesis , and left parenthesis 1 comma 0 right parenthesis

(0,0)
and (1,0)
left parenthesis 0 comma 0 right parenthesis and left parenthesis 1 comma 0 right parenthesis
Skip to navigation

Answer 1

To determine the points that can be used to find the quadratic equation modeling the height of the ball being dropped, we need key points based on the context of the problem.

1. The initial height from which the ball is dropped is 16 feet, which corresponds to the point (0, 16).
2. The height of the ball is expected to reach 0 feet when it has hit the ground, which corresponds to the point (1, 0) if we assume it hits the ground at 1 second.

Therefore, the two important points we need are (0, 16) and (1, 0).

The point (0.375, 14) can provide additional detail about the trajectory but is not necessary to establish the basic quadratic model.

Thus, the most suitable response is:

(0, 16), (0.375, 14), and (1, 0).

This choice includes the start point and the point where the ball hits the ground, as well as an additional point on the path.