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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)
, (0.375,14)
, 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
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Answer 1

To model the height of a ball being dropped from a height of 16 feet using a quadratic equation, we need points that reflect the initial height, the decreasing height at certain times, and the point when the ball hits the ground (height = 0).

Given the options, the most appropriate set of points to represent this scenario is:

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

• (0,16) represents the initial height of the ball before it is dropped.
• (0.5,12) indicates the height of the ball at 0.5 seconds.
• (1,0) shows that the ball reaches the ground (height = 0) at 1 second.

Thus, the correct option is:

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