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 need to determine the vertices of the function $ 13c(x) $.

Multiplying a function by a constant, in this case, 13, only scales the output values (the $ y $-coordinates) by that constant. The $ x $-coordinates of the vertices remain the same.

### Calculating the new vertices:
1. The first vertex at $(-3, 1)$:
   - New $ y $-coordinate: $ 13 \times 1 = 13 $
   - New vertex: $(-3, 13)$

2. The second vertex at $(2, -9)$:
   - New $ y $-coordinate: $ 13 \times (-9) = -117 $
   - New vertex: $(2, -117)$

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

Would you like more details or have any other questions?

Here are 5 related questions to consider:
1. How do transformations affect the graph of a cubic function?
2. What happens to the shape of the cubic function when it is multiplied by a negative constant?
3. How do you find the roots of a cubic function given its graph?
4. What is the significance of the vertex in the context of a cubic function?
5. How does adding a constant to a cubic function affect its graph?

**Tip:** When multiplying a function by a constant, always remember that only the $ y $-values are scaled, not the $ x $-values.

Explore how to find the vertices of the function 13c(x) given the vertices of c(x) are (-3, 1) and (2, -9). Understand the transformation of functions and how scaling affects the y-coordinates of vertices.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation