Question 4 100 Points Use transformations to graph the function. Show all the steps, each on it's own graph along with its respective equation. u (x) = -(x – 1)² – 2 ...
Question 4 100 Points Use transformations to graph the function. Show all the steps, each on it's own graph along with its respective equation. u (x) = -(x – 1)² – 2 ...
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Question 4**
**100 Points**
Use transformations to graph the function. Show all the steps, each on its own graph along with its respective equation.
\[ u(x) = -(x - 1)^2 - 2 \]
### Explanation:
To graph the function \( u(x) = -(x - 1)^2 - 2 \) using transformations, you start with the basic quadratic function \( f(x) = x^2 \) and apply the following steps:
1. **Horizontal Shift**: Replace \( x \) with \( x - 1 \) to shift the graph 1 unit to the right.
- Equation: \( (x - 1)^2 \)
2. **Vertical Flip**: Multiply the entire function by \(-1\) to reflect the graph over the x-axis.
- Equation: \( -(x - 1)^2 \)
3. **Vertical Shift**: Subtract 2 from the entire function to shift the graph 2 units downward.
- Final Equation: \( -(x - 1)^2 - 2 \)
Each transformation should be shown on a separate graph, displaying the progression from the basic function to the transformed function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4931441c-10c9-4e0d-964b-11065e671b38%2Fec7ade3c-0ec0-4cca-af7d-abd978be80cb%2Fgnhsam_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 4**
**100 Points**
Use transformations to graph the function. Show all the steps, each on its own graph along with its respective equation.
\[ u(x) = -(x - 1)^2 - 2 \]
### Explanation:
To graph the function \( u(x) = -(x - 1)^2 - 2 \) using transformations, you start with the basic quadratic function \( f(x) = x^2 \) and apply the following steps:
1. **Horizontal Shift**: Replace \( x \) with \( x - 1 \) to shift the graph 1 unit to the right.
- Equation: \( (x - 1)^2 \)
2. **Vertical Flip**: Multiply the entire function by \(-1\) to reflect the graph over the x-axis.
- Equation: \( -(x - 1)^2 \)
3. **Vertical Shift**: Subtract 2 from the entire function to shift the graph 2 units downward.
- Final Equation: \( -(x - 1)^2 - 2 \)
Each transformation should be shown on a separate graph, displaying the progression from the basic function to the transformed function.
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