The vertices of cubic function c(x) are located at (−3,1)
 and (2,−9)
 Where are the vertices of 13c(x)
 located? Enter your responses as ordered pairs. Do not include any spaces.

The function \( 13c(x) \) represents a vertical stretch of the function \( c(x) \) by a factor of 13. This transformation affects the **y-coordinates** of the points but does **not** affect the x-coordinates.

### Original vertices of \( c(x) \):
- \( (-3, 1) \)
- \( (2, -9) \)

### Applying the vertical stretch:
For the vertex \( (-3, 1) \), the y-coordinate becomes \( 13 \times 1 = 13 \), so the new vertex is \( (-3, 13) \).

For the vertex \( (2, -9) \), the y-coordinate becomes \( 13 \times (-9) = -117 \), so the new vertex is \( (2, -117) \).

### Final answer:
The vertices of \( 13c(x) \) are \( (-3,13) \) and \( (2,-117) \).

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Would you like more details on vertical stretching or any other part of the solution? 

Here are five related questions you might explore:
1. How do horizontal stretches or compressions affect a cubic function's graph?
2. What effect does reflecting a function across the x-axis have on its vertices?
3. If the cubic function was translated, how would the new vertex positions be determined?
4. What happens to the shape of the cubic function when only the y-coordinates are stretched?
5. How does scaling affect the critical points of the cubic function?

**Tip:** Vertical scaling by a factor of \( k \) multiplies every y-coordinate by \( k \), but the x-coordinates remain unchanged.

The vertices of cubic function c(x) are located at (−3,1) and (2,−9). Where are the vertices of 13c(x) located? Enter your responses as ordered pairs. Do not include any spaces.

Explore how the vertices of the cubic function c(x), originally located at (-3,1) and (2,-9), are transformed when applying a vertical stretch by a factor of 13. This problem involves key concepts of transformations and vertical scaling in algebra, suitable for students in Grades 9-12.

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