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 function \( 13c(x) \) is a vertical stretch of the cubic function \( c(x) \) by a factor of 13. A vertical stretch only affects the y-coordinates of the points, leaving the x-coordinates unchanged. Since the vertices of the original function \( c(x) \) are at \( (-3, 1) \) and \( (2, -9) \), applying the vertical stretch by 13 will multiply the y-coordinates by 13 while keeping the x-coordinates the same.

Thus, the new vertices of \( 13c(x) \) will be:

1. For \( (-3, 1) \), the new vertex is \( (-3, 1 \times 13) = (-3, 13) \).
2. For \( (2, -9) \), the new vertex is \( (2, -9 \times 13) = (2, -117) \).

Therefore, the vertices of \( 13c(x) \) are located at:

\[
(-3,13) \quad \text{and} \quad (2,-117)
\]

Let me know if you need further details or have any questions!

Here are some related questions to further explore:

1. What happens to the roots of the function under vertical stretching?
2. How does horizontal stretching affect the vertices of a cubic function?
3. Can you express \( 13c(x) \) in terms of transformations applied to \( c(x) \)?
4. How would the graph of \( c(x) \) change if a vertical compression instead of a stretch was applied?
5. How do the x-intercepts of \( 13c(x) \) relate to those of \( c(x) \)?

**Tip:** Vertical stretching multiplies only the y-coordinates, while horizontal transformations affect 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.

Find the vertices of the cubic function 13c(x) when the original function's vertices are at (-3, 1) and (2, -9). This problem demonstrates how vertical stretching by a factor of 13 affects the y-coordinates of the cubic function's vertices. Suitable for high school students learning transformations in Algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation