Question
The graph represents the height y, in feet, above the ground of a water balloon x seconds after it is dropped from a window.
Which statements are true?
Select each correct answer.
Responses
The maximum height of the water balloon occurs at x = 0.
The maximum height of the water balloon occurs at x = 0.
The maximum height of the water balloon is 64 ft.
The maximum height of the water balloon is 64 ft.
The water balloon is in the air for 2 s.
The water balloon is in the air for 2 s.
The water balloon rises above 64 ft before falling toward the ground.
The water balloon rises above 64 ft before falling toward the ground.
The water balloon hits the ground in 64 s.
The water balloon hits the ground in 64 s.
A parabola is graphed on a coordinate plane. The horizontal x-axis is labeled Time in seconds and ranges from 0 to 4 in increments of 1. The vertical y-axis is labeled Height in meters and ranges from 0 to 64 in increments of 4. The vertex is located at begin ordered pair 0 comma 64 end ordered pair. The parabola opens downward. It passes through the horizontal axis at begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma 64 end ordered pair.
Which statements are true?
Select each correct answer.
Responses
The maximum height of the water balloon occurs at x = 0.
The maximum height of the water balloon occurs at x = 0.
The maximum height of the water balloon is 64 ft.
The maximum height of the water balloon is 64 ft.
The water balloon is in the air for 2 s.
The water balloon is in the air for 2 s.
The water balloon rises above 64 ft before falling toward the ground.
The water balloon rises above 64 ft before falling toward the ground.
The water balloon hits the ground in 64 s.
The water balloon hits the ground in 64 s.
A parabola is graphed on a coordinate plane. The horizontal x-axis is labeled Time in seconds and ranges from 0 to 4 in increments of 1. The vertical y-axis is labeled Height in meters and ranges from 0 to 64 in increments of 4. The vertex is located at begin ordered pair 0 comma 64 end ordered pair. The parabola opens downward. It passes through the horizontal axis at begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma 64 end ordered pair.
Answers
GPT-4o mini
Based on the description of the graph, we can evaluate each statement:
1. **The maximum height of the water balloon occurs at x = 0.**
- True. The vertex of the parabola, which represents the maximum height, is at the point (0, 64), meaning the maximum height occurs at x = 0.
2. **The maximum height of the water balloon is 64 ft.**
- True. The vertex has a y-coordinate of 64, indicating the maximum height of the water balloon is 64 feet.
3. **The water balloon is in the air for 2 s.**
- True. The balloon is at a height of 0 feet at x = 2 seconds, which indicates that it hits the ground at 2 seconds.
4. **The water balloon rises above 64 ft before falling toward the ground.**
- False. Since the maximum height remains at 64 feet and is reached immediately at the time of release (x = 0), the water balloon does not rise above 64 ft.
5. **The water balloon hits the ground in 64 s.**
- False. The water balloon hits the ground at x = 2 seconds, not 64 seconds.
Based on this analysis, the true statements are:
- The maximum height of the water balloon occurs at x = 0.
- The maximum height of the water balloon is 64 ft.
- The water balloon is in the air for 2 s.
1. **The maximum height of the water balloon occurs at x = 0.**
- True. The vertex of the parabola, which represents the maximum height, is at the point (0, 64), meaning the maximum height occurs at x = 0.
2. **The maximum height of the water balloon is 64 ft.**
- True. The vertex has a y-coordinate of 64, indicating the maximum height of the water balloon is 64 feet.
3. **The water balloon is in the air for 2 s.**
- True. The balloon is at a height of 0 feet at x = 2 seconds, which indicates that it hits the ground at 2 seconds.
4. **The water balloon rises above 64 ft before falling toward the ground.**
- False. Since the maximum height remains at 64 feet and is reached immediately at the time of release (x = 0), the water balloon does not rise above 64 ft.
5. **The water balloon hits the ground in 64 s.**
- False. The water balloon hits the ground at x = 2 seconds, not 64 seconds.
Based on this analysis, the true statements are:
- The maximum height of the water balloon occurs at x = 0.
- The maximum height of the water balloon is 64 ft.
- The water balloon is in the air for 2 s.