### Problem Statement**Given the parent function** \( f(x) = x^2 \), **which of the functions listed below would be an equivalent function that has been translated right 3 and up 2?**1. \( g(x) = (x - 3)^2 - 2 \)2. \( g(x) = (x + 3)^2 + 2 \)3. \( g(x) = (x - 3)^2 + 2 \)4. \( g(x) = (x + 3)^2 - 2 \)### ExplanationWhen translating the parent function \( f(x) = x^2 \):- **Right by 3 units**: We replace \( x \) with \( (x - 3) \) in the function.- **Up by 2 units**: We add 2 to the function.Combining these transformations, we get the function:\[ g(x) = (x - 3)^2 + 2 \]Thus, the correct answer is:- **Option 3: \( g(x) = (x - 3)^2 + 2 \)**

To find:The given function is translated 3 units right and 2 units upNote:Translation of FunctionsA…

Answered: Given the parent function f(x) = x²,…

Given the parent function f(x) = x², which of the functions listed below would be an equivalent function that has been translated right 3 and up 2? ○g(x) = (x − 3)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

### Problem Statement

**Given the parent function** \( f(x) = x^2 \), **which of the functions listed below would be an equivalent function that has been translated right 3 and up 2?**

1. \( g(x) = (x - 3)^2 - 2 \)

2. \( g(x) = (x + 3)^2 + 2 \)

3. \( g(x) = (x - 3)^2 + 2 \)

4. \( g(x) = (x + 3)^2 - 2 \)

### Explanation
When translating the parent function \( f(x) = x^2 \):

- **Right by 3 units**: We replace \( x \) with \( (x - 3) \) in the function.
- **Up by 2 units**: We add 2 to the function.

Combining these transformations, we get the function:
\[ g(x) = (x - 3)^2 + 2 \]

Thus, the correct answer is:
- **Option 3: \( g(x) = (x - 3)^2 + 2 \)**

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