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,...
Related questions
Question
![### Transformation of the Parent Function
**Problem Statement:**
Write an equation for the transformation of the parent function.
**Graph Description:**
The graph depicts a quadratic function that has been transformed. The red curve indicates the transformed function \( g(x) \). The coordinate axes are marked, and significant transformations including translations and reflections are observable. The graph appears to be a parabola that opens downwards, indicating a transformation involving reflecting across the x-axis.
**Given Options:**
The equation of the transformed function \( g(x) \) is to be chosen from the following options:
1. \( g(x) = -(x - 4)^2 + 2 \)
2. \( g(x) = -(x + 4)^2 + 2 \)
3. \( g(x) = -(x - 2)^2 + 2 \)
4. \( g(x) = -(x + 4)^2 - 2 \)
5. \( g(x) = -(x - 2)^2 - 4 \)
**Analysis:**
The provided graph shows the transformed quadratic function. The following steps can be used to determine the correct equation:
1. Identify the vertex of the parabola.
2. Determine the direction of the parabola (upwards or downwards).
3. Match the vertex and direction with one of the provided options.
**Explanation of Graph:**
- The vertex of the parabola is at \( (4, 2) \), and it opens downwards. Therefore, the equation must have the form \( (x - 4) \) inside the square term and a negative sign outside the square term.
- Thus, the correct option is:
\[
g(x) = -(x - 4)^2 + 2
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F941eb469-a862-4ae1-815d-a6698b94400a%2Fe902bac9-47e9-4225-b753-9949f8bcc426%2Frmnu9rk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Transformation of the Parent Function
**Problem Statement:**
Write an equation for the transformation of the parent function.
**Graph Description:**
The graph depicts a quadratic function that has been transformed. The red curve indicates the transformed function \( g(x) \). The coordinate axes are marked, and significant transformations including translations and reflections are observable. The graph appears to be a parabola that opens downwards, indicating a transformation involving reflecting across the x-axis.
**Given Options:**
The equation of the transformed function \( g(x) \) is to be chosen from the following options:
1. \( g(x) = -(x - 4)^2 + 2 \)
2. \( g(x) = -(x + 4)^2 + 2 \)
3. \( g(x) = -(x - 2)^2 + 2 \)
4. \( g(x) = -(x + 4)^2 - 2 \)
5. \( g(x) = -(x - 2)^2 - 4 \)
**Analysis:**
The provided graph shows the transformed quadratic function. The following steps can be used to determine the correct equation:
1. Identify the vertex of the parabola.
2. Determine the direction of the parabola (upwards or downwards).
3. Match the vertex and direction with one of the provided options.
**Explanation of Graph:**
- The vertex of the parabola is at \( (4, 2) \), and it opens downwards. Therefore, the equation must have the form \( (x - 4) \) inside the square term and a negative sign outside the square term.
- Thus, the correct option is:
\[
g(x) = -(x - 4)^2 + 2
\]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education