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.

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=x^2
 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=x^2
 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=x^2
 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=x^2
 due to the changes in the y-intercept.

GPT-4o mini · Answer

The correct interpretation of the transformation that occurred from the parent function \( y = x^2 \) is:

This is a vertical stretch of the parent function \( y=x^2 \) due to the changes in the y-coordinates of each point.

A vertical stretch would imply that the values of \( y \) increase more rapidly than they would for the standard \( y = x^2 \) function, affecting the y-coordinates of the points plotted on the graph, while the x-coordinates dictate the horizontal positioning of the parabola but do not influence the vertical stretching directly.