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.

Question

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
; compression
0.5 x ; compression

0.5x
; stretch
0.5 x ; stretch

0.5; compression

Answer 1

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

In general, the transformation of a function of the form \( f(x) = ax^2 \) can be affected by the coefficient \( a \):

• If \( |a| > 1 \), the parabola undergoes a vertical stretch.
• If \( 0 < |a| < 1 \), the parabola undergoes a vertical compression.

Since the value of \( k \) is not directly provided in your question, we can infer it if we assume \( k \) refers to the coefficient \( a \) of the transformed parabolas.

Given the options and focus on the value of \( k \):

• The only option that suggests \( k = 0.5 \) is 0.5; compression and 0.5; stretch.

Based on the definitions above, since \( k = 0.5 \) implies \( 0 < k < 1 \), it corresponds to a vertical compression.

Therefore, the correct response is:

0.5; compression.