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

The transformation \( \frac{1}{3}c(x) \) represents a vertical scaling of the cubic function \( c(x) \) by a factor of \( \frac{1}{3} \). This affects the y-values of the vertices, but the x-values remain unchanged.

Given the vertices of \( c(x) \) at \( (-3,1) \) and \( (2,-9) \), we apply the vertical scaling to the y-values only:

1. For the vertex \( (-3,1) \), scaling the y-coordinate by \( \frac{1}{3} \):
   \[
   1 \times \frac{1}{3} = \frac{1}{3}
   \]
   So, the new vertex is \( (-3, \frac{1}{3}) \).

2. For the vertex \( (2,-9) \), scaling the y-coordinate by \( \frac{1}{3} \):
   \[
   -9 \times \frac{1}{3} = -3
   \]
   So, the new vertex is \( (2, -3) \).

Thus, the vertices of \( \frac{1}{3}c(x) \) are located at \( (-3,\frac{1}{3}) \) and \( (2,-3) \).

The final answer is:

**\( (-3,\frac{1}{3}) \) and \( (2,-3) \)**.

Would you like any additional details or clarifications?

Here are 5 related questions to explore:
1. How do horizontal transformations affect the vertices of a function?
2. What effect would reflecting \( c(x) \) over the x-axis have on the vertices?
3. How do you find the equation of a cubic function given its vertices?
4. How do horizontal scaling transformations affect the graph of a cubic function?
5. What role do inflection points play in the shape of a cubic function?

**Tip:** Vertical scaling only affects the y-values of the graph, leaving the x-values unchanged.

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

Find out how to determine the new vertices of the cubic function c(x) after applying a vertical scaling by 1/3. This solution explains key concepts like vertical scaling and transformations, with step-by-step guidance for students in Grades 10-12.

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