Use the image to answer the question.

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-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-intercept.
This is a vertical stretch of the parent function y equals x squared due to the changes in the y -intercept.

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 x-intercept.

Answer 1

The correct interpretation of the key features of the graph, considering that it is an upward-opening parabola that has been transformed from the parent function \(y = x^2\), would be:

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 means that the values of \(y\) are being multiplied by a factor greater than 1, which corresponds to an increase in the distance between the graph and the x-axis compared to the parent function. The transformation affects the y-coordinates, which reflects the value of the function at each corresponding x-coordinate.