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.
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The equation is f left parenthesis x right parenthesis equals 4 times x squared. The coordinates of the plotted points are labeled as left parenthesis negative 2 comma 16 right parenthesis, left parenthesis negative 1 comma 4 right parenthesis, vertex at left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 4 right parenthesis, and left parenthesis 2 comma 16 right parenthesis.

Interpret the key features of the graph. What type of transformation occurred from the parent function?

(1 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=x2
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=x2
due to the changes in the y-coordinates of each point.

Answer 1

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

Reason: f(x)=4x^2 multiplies every y-value by 4 (e.g., (1,1) → (1,4), (2,4) → (2,16)), so the y-coordinates change while x-coordinates stay the same.