Question
Analyzing a Graph Quick Check
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Question
Use the image to answer the question.
An upward open parabola passes through 5 plotted points on a coordinate plane with x-axis ranging from negative 12 to 12 in increments of 2 and y-axis ranging from negative 6 to 18 in increments of 2.
Interpret the key features of the graph. What type of transformation occurred from the parent function?
(1 point)
Responses
This is a vertical stretch of the parent function y=x2
due to the changes in the x-intercept.
This is a vertical stretch of the parent function y equals x squared due to the changes in the x- intercept.
This is a vertical stretch of the parent function y=x2
due to the changes in the x-coordinates of each point.
This is a vertical stretch of the parent function y equals x squared due to the changes in the x -coordinates of each point.
This is a vertical stretch of the parent function y=x2
due to the changes in the y-coordinates of each point.
This is a vertical stretch of the parent function y equals x squared due to the changes in the y -coordinates of each point.
This is a vertical stretch of the parent function y=x2
due to the changes in the y-intercept.
This is a vertical stretch of the parent function y equals x squared due to the changes in the y -intercept.
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Answers
Answered by
GPT-4o mini
To interpret the key features of the graph of a parabola and the transformation from the parent function \( y = x^2 \), it's essential to focus on the nature of the vertical stretch and how the coordinates of the points change compared to the parent function.
In this case, since you're examining a vertical stretch of the graph, you need to consider how the y-coordinates of the points on the graph are affected. The vertical stretch indicates that the parabola has been stretched away from the x-axis, making the y-coordinates larger compared to their corresponding x-values in the parent function.
Given the possible responses, the correct choice would emphasize the changes in the y-coordinates as the reason for the vertical stretch. The best answer is:
**This is a vertical stretch of the parent function y = x^2 due to the changes in the y-coordinates of each point.**
This response accurately reflects how the vertical stretch modifies the graph relative to the parent function.
In this case, since you're examining a vertical stretch of the graph, you need to consider how the y-coordinates of the points on the graph are affected. The vertical stretch indicates that the parabola has been stretched away from the x-axis, making the y-coordinates larger compared to their corresponding x-values in the parent function.
Given the possible responses, the correct choice would emphasize the changes in the y-coordinates as the reason for the vertical stretch. The best answer is:
**This is a vertical stretch of the parent function y = x^2 due to the changes in the y-coordinates of each point.**
This response accurately reflects how the vertical stretch modifies the graph relative to the parent function.