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 vertices of the cubic function \( c(x) \) are given at \( (-3, 1) \) and \( (2, -9) \). When you multiply a function by a constant, like \( 13 \), the \( x \)-coordinates of the vertices remain the same, but the \( y \)-coordinates are scaled by the constant.

So, for the function \( 13c(x) \):
- The vertex at \( (-3, 1) \) becomes \( (-3, 13 \times 1) = (-3, 13) \).
- The vertex at \( (2, -9) \) becomes \( (2, 13 \times (-9)) = (2, -117) \).

Thus, the vertices of \( 13c(x) \) are:
\[
(-3,13) \quad \text{and} \quad (2,-117)
\]

Would you like further details on how scaling functions affect their graphs, or have any other questions?

Here are 5 related questions for deeper understanding:
1. How does scaling a function vertically by a constant affect its graph?
2. What happens to the roots of a function when it is multiplied by a constant?
3. Can you identify other transformations that might affect both \( x \)- and \( y \)-coordinates of the vertices?
4. How does multiplying a function by a negative constant impact its graph?
5. What are the steps to find the turning points of a cubic function?

**Tip:** Multiplying a function by a constant only affects the vertical scaling, leaving horizontal positions (such as \( x \)-coordinates) 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.

Learn how to determine the new vertex positions of a cubic function c(x) when scaled by a constant, 13. This detailed solution explains how to apply vertical scaling, leaving x-coordinates unchanged while multiplying y-coordinates by the constant. Ideal for Grades 10-12.

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