### 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: \[ g(x) = -(x - 4)^2 + 2 \]

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Write an equation for the transformation of the parent function. 6 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

### 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:
\[
g(x) = -(x - 4)^2 + 2
\]

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