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

The given vertices of the cubic function \( c(x) \) are located at \( (-3, 1) \) and \( (2, -9) \). We are asked to find the vertices of the function \( 13c(x) \), which is the original function scaled vertically by a factor of 13.

### Step-by-step analysis:

1. **Understanding the transformation:**
   - The function \( 13c(x) \) means the entire graph of \( c(x) \) is stretched vertically by a factor of 13. 
   - Vertices occur at specific x-values, and since the transformation is vertical, **the x-values of the vertices remain unchanged**.
   - However, the **y-values will be scaled by 13**.

2. **Calculating the new y-values:**
   - For the vertex \( (-3, 1) \), the y-value becomes:
     \[
     13 \times 1 = 13
     \]
     So, the new vertex is \( (-3, 13) \).
   
   - For the vertex \( (2, -9) \), the y-value becomes:
     \[
     13 \times (-9) = -117
     \]
     So, the new vertex is \( (2, -117) \).

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

Would you like more details or have any questions?

Here are 5 related questions:
1. How does a horizontal scaling affect the coordinates of the vertices?
2. What is the effect of a negative scalar on the function \( c(x) \)?
3. If the function was shifted vertically, how would the vertices change?
4. What is the general form of a cubic function, and how are its vertices identified?
5. How does vertical stretching/compression differ from horizontal transformations?

**Tip:** Always analyze whether transformations affect the x-values or y-values depending on whether they are horizontal or vertical!

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.

Explore how to find the new vertices of the cubic function c(x) after applying a vertical scaling factor. The original vertices are at (-3, 1) and (2, -9), and the function is scaled by a factor of 13. Suitable for high school students in Grades 10-12, this problem involves algebraic transformations of cubic functions.

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