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

(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

(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

(16,0)
, (12,0.5)
, and (0,1)

Answer 1

To find the quadratic equation that models the height of a ball being dropped, we need to identify points that represent the initial height, the height at specific times, and the time when the ball reaches the ground (height = 0).

Given the scenario:

• The ball starts from a height of 16 feet at time \( t = 0 \) seconds. This gives us the point \( (0, 16) \).
• At some point between 0 and 1.25 seconds, the height of the ball decreases. In the options given, point \( (0.375, 14) \) indicates that at \( t = 0.375 \) seconds, the height is 14 feet.
• Finally, the ball reaches the ground at time \( t = 1 \) second, which corresponds to the point \( (1, 0) \).

Thus, the points that can be used to find the quadratic equation are \( (0, 16) \), \( (0.375, 14) \), and \( (1, 0) \).

Therefore, the correct option is:

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