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.

The vertices of the cubic function \( c(x) \) are given as \( (-3, 1) \) and \( (2, -9) \). To determine the vertices of \( \frac{1}{3}c(x) \), we need to understand the transformation applied to \( c(x) \).

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

### Calculation:
- For the vertex \( (-3, 1) \):
  \[
  y \text{ coordinate changes to } \frac{1}{3} \times 1 = \frac{1}{3}
  \]
  New vertex: \( \left(-3, \frac{1}{3}\right) \)

- For the vertex \( (2, -9) \):
  \[
  y \text{ coordinate changes to } \frac{1}{3} \times -9 = -3
  \]
  New vertex: \( (2, -3) \)

### Answer:
The vertices of \( \frac{1}{3}c(x) \) are located at \( \left(-3,\frac{1}{3}\right) \) and \( (2,-3) \).

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How does a horizontal compression affect the vertices of a cubic function?
2. What is the general effect of multiplying a function by a constant \( k \) on its graph?
3. How would you find the zeros of the transformed function \( \frac{1}{3}c(x) \)?
4. If the function was vertically stretched by a factor of 2 instead, what would the new vertices be?
5. What is the effect of reflecting the function \( c(x) \) over the x-axis on its vertices?

**Tip:** Remember, vertical transformations (stretching or compressing) only affect the y-coordinates of the points on the graph, not the x-coordinates.

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.

Learn how to determine the vertices of the transformed cubic function 1/3c(x) given the original vertices at (-3, 1) and (2, -9). This problem involves understanding vertical compressions and how they affect function graphs. Suitable for students in Grades 10-12.

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