Question

Use the image to answer the 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
; compression
0.5 x ; compression

0.5; compression
0.5; compression

0.5x
; stretch
0.5 x ; stretch
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Answer 1

To determine the value of \( k \) and whether the transformation shows a stretch or compression, consider the general form of a parabola in relation to transformations.

1. **Value of \( k \)**: In the context of parabolas, a value of \( k \) typically represents a vertical scaling factor. If \( k < 1 \) (like \( 0.5 \)), the parabola is compressed. If \( k > 1 \), it indicates a vertical stretch of the parabola.

2. **Stretch vs. Compression**:
- If \( k = 0.5 \), the parabola would be compressed vertically, making it "wider" than the original.

Given these points:

- If \( k = 0.5 \), it is a compression.
- Therefore, the correct transformation is:

**0.5; compression**

So the right choice is:
**0.5; compression**