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 \( c(x) \) is a cubic function, and you are asked to find the vertices of the transformed function \( 13c(x) \).

### Key concept:
Multiplying a function by a constant, such as \( 13 \), only affects the **y-coordinates** of points on the graph, scaling them vertically. The x-coordinates remain unchanged.

### Solution:
The vertices of the function \( c(x) \) are given as:
- \( (-3, 1) \)
- \( (2, -9) \)

When the function is scaled by 13, the y-coordinates of these points are multiplied by 13, while the x-coordinates remain the same.

1. For \( (-3, 1) \), the new y-coordinate is:
   \[
   13 \times 1 = 13
   \]
   So, the new vertex is \( (-3, 13) \).

2. For \( (2, -9) \), the new y-coordinate is:
   \[
   13 \times (-9) = -117
   \]
   So, the new vertex is \( (2, -117) \).

### Final Answer:
The vertices of \( 13c(x) \) are located at:
\[
(-3,13) \quad \text{and} \quad (2,-117)
\]

Would you like further clarification or details? 

Here are 5 related questions:
1. What happens if we multiply the function by a negative constant?
2. How does translating a function horizontally affect its graph?
3. What is the effect of scaling the function horizontally instead of vertically?
4. Can we find the equation of \( c(x) \) given more information?
5. How do transformations affect the roots of a cubic function?

**Tip**: Always remember that multiplying a function by a constant only stretches or compresses it vertically, not horizontally.

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.

Learn how to find the new vertices of a cubic function when it is scaled by a factor of 13. The vertices of the original function c(x) are located at (−3,1) and (2,−9). Explore how vertical scaling affects the y-coordinates of a function while keeping x-coordinates unchanged. Suitable for students in Grades 9-12.

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