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 10:** Which choice describes the translation of \( y = x^2 \) to \( y = (x + 4)^2 \)?
**Options:**
- ○ 4 units down
- ○ 4 units right
- ○ 4 units up
- ○ 4 units left
---
In this question, students are asked to determine the type of translation that has been applied to the function. The original function is \( y = x^2 \), and it is translated to \( y = (x + 4)^2 \).
### Explanation of the Translation:
The equation \( y = (x + 4)^2 \) represents a horizontal translation of the function \( y = x^2 \). The \( +4 \) inside the parentheses indicates a shift to the left by 4 units.
When a number is added directly to the input variable \( x \) inside the function, it results in a horizontal shift in the opposite direction of the sign. Thus, in this case:
- **4 units left** is the correct description of this translation.
This concept is important in understanding how changes within the function can move the graph on the coordinate plane without altering its shape.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96e0847f-4973-4b99-ac1e-7e94417321c7%2F929d2c96-963a-403c-9f62-9003e773703c%2Fom1oy39_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 10:** Which choice describes the translation of \( y = x^2 \) to \( y = (x + 4)^2 \)?
**Options:**
- ○ 4 units down
- ○ 4 units right
- ○ 4 units up
- ○ 4 units left
---
In this question, students are asked to determine the type of translation that has been applied to the function. The original function is \( y = x^2 \), and it is translated to \( y = (x + 4)^2 \).
### Explanation of the Translation:
The equation \( y = (x + 4)^2 \) represents a horizontal translation of the function \( y = x^2 \). The \( +4 \) inside the parentheses indicates a shift to the left by 4 units.
When a number is added directly to the input variable \( x \) inside the function, it results in a horizontal shift in the opposite direction of the sign. Thus, in this case:
- **4 units left** is the correct description of this translation.
This concept is important in understanding how changes within the function can move the graph on the coordinate plane without altering its shape.
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