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:**
Transform the equation \( y = x^2 + 8x + 15 \) into the vertex form \( y = (x-h)^2 + k \).
**Answer Form:**
\[ y = \]
**Explanation:**
To convert the quadratic equation from standard form to vertex form, we complete the square.
1. Start with the equation \( y = x^2 + 8x + 15 \).
2. Focus on the \( x^2 + 8x \) part. To complete the square:
- Take half of the coefficient of \( x \) (which is 8), giving 4, and square it to get 16.
3. Add and subtract 16 inside the equation:
- \( y = (x^2 + 8x + 16) - 16 + 15 \).
4. Rewrite the quadratic expression as a perfect square:
- \( y = (x + 4)^2 - 1 \).
Now, the equation is in the vertex form \( y = (x-h)^2 + k \), where \( h = -4 \) and \( k = -1 \).
**Final Answer:**
\[ y = (x+4)^2 - 1 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf99ef9a-11bc-4c83-b49c-a6b52894d845%2Fffaba68a-5dda-4902-9765-ec4cbd74c4fd%2Fct8pvxo_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Transform the equation \( y = x^2 + 8x + 15 \) into the vertex form \( y = (x-h)^2 + k \).
**Answer Form:**
\[ y = \]
**Explanation:**
To convert the quadratic equation from standard form to vertex form, we complete the square.
1. Start with the equation \( y = x^2 + 8x + 15 \).
2. Focus on the \( x^2 + 8x \) part. To complete the square:
- Take half of the coefficient of \( x \) (which is 8), giving 4, and square it to get 16.
3. Add and subtract 16 inside the equation:
- \( y = (x^2 + 8x + 16) - 16 + 15 \).
4. Rewrite the quadratic expression as a perfect square:
- \( y = (x + 4)^2 - 1 \).
Now, the equation is in the vertex form \( y = (x-h)^2 + k \), where \( h = -4 \) and \( k = -1 \).
**Final Answer:**
\[ y = (x+4)^2 - 1 \]
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