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

0.5; compression
0.5; compression

0.5x
; compression
0.5 x ; compression

0.5x
; stretch

Answer 1

To determine the value of \( k \) and whether the transformation indicates a stretch or a compression, we need to analyze the given information about the parabolas.

1. Since the parabolas are opening upward and both begin in quadrant 2, it suggests they are both concave and symmetric around their vertices. If the parabolas share a common vertex on the y-axis, it's likely that their vertical scaling factor \( k \) affects their height.

2. The nature of the transformation will be determined by the value of \( k \). In quadratic functions, if \( k < 1 \), it usually results in a compression (the parabola becomes wider). If \( k > 1 \), it results in a stretch (the parabola becomes narrower).

3. You mentioned that the value of \( k \) is 0.5. Since 0.5 is less than 1, this indicates that the transformation is a compression.

Based on this analysis, the correct answer is:

0.5; compression.