The vertices of cubic function c(x) are located at (−3,1)
 and (2,−9)
 Where are the vertices of 13c(x)
 located? 

The vertices of the cubic function \( c(x) \) are located at \( (-3, 1) \) and \( (2, -9) \). When we scale the function vertically by a factor of 13, i.e., by considering the function \( 13c(x) \), the \( x \)-coordinates of the vertices remain unchanged, but the \( y \)-coordinates are scaled by 13.

Let's compute the new \( y \)-coordinates for each vertex:

1. For the vertex \( (-3, 1) \):
   \[
   y_{\text{new}} = 13 \cdot 1 = 13
   \]
   So the new vertex is \( (-3, 13) \).

2. For the vertex \( (2, -9) \):
   \[
   y_{\text{new}} = 13 \cdot (-9) = -117
   \]
   So the new vertex is \( (2, -117) \).

### Conclusion:
The vertices of the function \( 13c(x) \) are located at \( (-3, 13) \) and \( (2, -117) \).

Would you like further details on how the scaling affects the graph?

Here are five related questions:
1. How does scaling a function horizontally affect its vertices?
2. What would happen to the graph of \( c(x) \) if it were scaled by a negative factor?
3. How do you find the roots of a cubic function given its form?
4. What is the impact of scaling a function on its concavity and inflection points?
5. How does translating a function horizontally or vertically affect its critical points?

**Tip**: When scaling a function, only the values in the direction of the scaling (i.e., vertically or horizontally) change; the other coordinates stay the same.

The vertices of cubic function c(x) are located at (-3, 1) and (2, -9). Where are the vertices of 13c(x) located?

Discover how to locate the vertices of a cubic function after applying a vertical scaling transformation. This problem explores the effects of scaling on the function's vertices using key algebraic concepts. Suitable for high school students in Grades 10-12.

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