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.
$$ and $$

Given that the vertices of the cubic function $ c(x) $ are located at $ (-3, 1) $ and $ (2, -9) $, we are asked to find the vertices of $ 13c(x) $.

### Explanation:
When a function is multiplied by a constant (in this case, 13), it only affects the **y-coordinates** of the points. The transformation $ c(x) \to 13c(x) $ scales the function vertically by a factor of 13. This means that for every point $ (x, y) $ on the graph of $ c(x) $, the new point on the graph of $ 13c(x) $ will be $ (x, 13y) $.

### Applying this:
- The first vertex of $ c(x) $ is $ (-3, 1) $. Under the transformation, the new vertex becomes:
  \[
  (-3, 13 \times 1) = (-3, 13)
  \]
- The second vertex of $ c(x) $ is $ (2, -9) $. Under the transformation, the new vertex becomes:
  \[
  (2, 13 \times (-9)) = (2, -117)
  \]

### Final Answer:
The vertices of $ 13c(x) $ are located at $ (-3, 13) $ and $ (2, -117) $.

Would you like further details or have any questions?

Here are 5 related questions:
1. What happens to the x-coordinates when a function is vertically scaled?
2. How would a horizontal scaling affect the coordinates of the vertices?
3. What are the general effects of multiplying a function by a negative constant?
4. Can you find the equation of the cubic function given its vertices?
5. How would adding a constant to the cubic function affect the vertices?

**Tip:** Vertical transformations affect only the y-coordinates, while horizontal transformations change the x-coordinates.

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 find the new vertices of the cubic function c(x) after a vertical scaling by a factor of 13. Original vertices are given at (-3,1) and (2,-9), and the solution shows step-by-step how to adjust the y-coordinates. Suitable for Grades 9-12.

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