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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![### Completing the Square in Quadratic Functions
To understand how to solve quadratic functions by completing the square, consider the following expression:
\[ y^2 + 16y + \boxed{ \ } \]
**Task:** Fill in the blank with a number to make the expression a perfect square.
#### Steps to Complete the Square:
1. **Identify the coefficient of the linear term.**
In this case, the linear term is \( 16y \), so the coefficient is 16.
2. **Divide the coefficient by 2.**
\( \frac{16}{2} = 8 \)
3. **Square the result from step 2.**
\( 8^2 = 64 \)
By adding 64 to the expression, we turn it into a perfect square trinomial:
\[ y^2 + 16y + 64 \]
This trinomial can be factored into:
\[ (y + 8)^2 \]
So, the number that should be added to the expression to complete the square is **64**.
### Visualization:
There is also a visual sidebar on the right side of the screen that includes formatted text and options, indicating navigational and interactive elements of the educational platform. The current screen shows a quadratic equation, with an instruction to fill in the blank.
#### Additional Features:
- **Close Button (X):** To exit the module or dialog.
- **Minimize/Maximize Buttons:** To adjust the view of the learning module.
- **Back Button (⟳):** To revert to the previous screen.
- **Help Button (?):** To provide additional instructions or support.
This interactive environment aids students in understanding the concept of completing the square, accompanied by step-by-step guidance and functional tools for a better learning experience.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc3f58a8-8dfb-4cee-aa0a-39cd0da35c96%2Fb4789e79-b13c-4738-b356-563bddb1c501%2Ffr6kzme_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Completing the Square in Quadratic Functions
To understand how to solve quadratic functions by completing the square, consider the following expression:
\[ y^2 + 16y + \boxed{ \ } \]
**Task:** Fill in the blank with a number to make the expression a perfect square.
#### Steps to Complete the Square:
1. **Identify the coefficient of the linear term.**
In this case, the linear term is \( 16y \), so the coefficient is 16.
2. **Divide the coefficient by 2.**
\( \frac{16}{2} = 8 \)
3. **Square the result from step 2.**
\( 8^2 = 64 \)
By adding 64 to the expression, we turn it into a perfect square trinomial:
\[ y^2 + 16y + 64 \]
This trinomial can be factored into:
\[ (y + 8)^2 \]
So, the number that should be added to the expression to complete the square is **64**.
### Visualization:
There is also a visual sidebar on the right side of the screen that includes formatted text and options, indicating navigational and interactive elements of the educational platform. The current screen shows a quadratic equation, with an instruction to fill in the blank.
#### Additional Features:
- **Close Button (X):** To exit the module or dialog.
- **Minimize/Maximize Buttons:** To adjust the view of the learning module.
- **Back Button (⟳):** To revert to the previous screen.
- **Help Button (?):** To provide additional instructions or support.
This interactive environment aids students in understanding the concept of completing the square, accompanied by step-by-step guidance and functional tools for a better learning experience.
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