Interpret the key features of the graph. What type of transformation occurred from the parent function? the function: f(x)=4x^2 Points:(-1,4) , (1,4) , (-2,16) , (2,16) Vertex:(0,0)

Question

(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 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 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.

Answer 1

The function \( f(x) = 4x^2 \) is a vertical transformation of the parent function \( y = x^2 \). The key feature to note here is that the coefficient of \( 4 \) in front of \( x^2 \) indicates a vertical stretch.

When comparing the points given:

• The points on the graph of the parent function \( y = x^2 \) at \( x = -1 \) and \( x = 1 \) would give \( y = 1^2 = 1 \), while for \( f(x) = 4x^2 \), the outputs are \( f(-1) = 4 \) and \( f(1) = 4 \). This indicates that the \( y \)-values have been multiplied by \( 4 \), demonstrating the vertical stretch.
• Similarly, at \( x = -2 \) and \( x = 2 \), the parent function gives \( y = (-2)^2 = 4 \), but \( f(-2) = 4(-2)^2 = 16 \).

From this analysis, the correct response is:

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