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.
$$ and $$

The function $ c(x) $ is a cubic function, and its vertices are given at points $(-3, 1)$ and $(2, -9)$. 

When the function is scaled by a factor of 13, as in $ 13c(x) $, the x-coordinates of the vertices remain unchanged because the scaling factor affects only the y-values. Thus, the new vertices will have the same x-coordinates, but the y-coordinates will be scaled by the factor of 13.

### Original Vertices
1. First vertex: $(-3, 1)$
2. Second vertex: $(2, -9)$

### New Vertices After Scaling by 13
1. First vertex: The y-coordinate of $(-3, 1)$ is scaled by 13, so it becomes $(-3, 13 \times 1) = (-3, 13)$.
2. Second vertex: The y-coordinate of $(2, -9)$ is scaled by 13, so it becomes $(2, 13 \times -9) = (2, -117)$.

### Final Answer
The vertices of $ 13c(x) $ are located at:
\[
(-3,13) \quad \text{and} \quad (2,-117)
\]

Do you want more details or have any questions? 

Here are 5 related questions you might find interesting:
1. How would the vertex positions change if the function was scaled by a negative factor?
2. What happens to the roots of $ c(x) $ when multiplied by a constant?
3. Can you find the function $ c(x) $ given the vertices and a point on the curve?
4. How does scaling affect the concavity of a cubic function?
5. How would you determine the inflection point of the function $ 13c(x) $?

**Tip:** Scaling a function vertically by a factor of $ k $ only affects the y-coordinates of all 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 13c(x) located? Enter your responses as ordered pairs. Do not include any spaces.

Explore how to determine the vertices of a scaled cubic function. Given the vertices of the cubic function c(x) at (-3,1) and (2,-9), learn how to find the new vertices after scaling the function by 13. This problem involves key concepts of scaling functions and transformations, suitable for Grades 10-12 students.

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