Use the image to answer the question.

Question

Two parabolas that open upward are plotted on a coordinate plane. Both parabolas begin in quadrant 2 sloping downward from left to right, pass through quadrant 3 until reaching a common vertex on the y-axis, and then rise through quadrants 4 and 1.

According to the graph, what is the value of k? Does the transformation show a stretch or a compression?

(1 point)
Responses

0.5; stretch
0.5; stretch

0.5x
; stretch
0.5 x ; stretch

0.5x
; compression
0.5 x ; compression

0.5; compression

Answer 1

To determine the value of \( k \) and whether the transformation shows a stretch or a compression, we need to understand how the parabolas are transformed.

When you have a parabola in standard form, such as \( y = ax^2 \), the value of \( k \) in the transformation \( y = kx^2 \) indicates whether a vertical compression or stretch is being applied:

• If \( |k| < 1 \), the parabola is compressed (it becomes "flatter").
• If \( |k| > 1 \), the parabola is stretched (it becomes narrower).

Since we are considering \( k = 0.5 \):

• Since \( 0.5 < 1 \), this indicates a compression.

Given this information, the answer would be:

0.5; compression