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,...
Related questions
Question
![**Question:**
Convert this into a quadratic in standard form. State a, b, and c for your solution.
\[ 3(x - 2)^2 + 1 = 28 \]
**Answer:**
Begin by expanding the expression on the left-hand side:
1. Expand \((x - 2)^2\):
\[
(x - 2)^2 = x^2 - 4x + 4
\]
2. Multiply the entire expression by 3:
\[
3(x^2 - 4x + 4) = 3x^2 - 12x + 12
\]
3. Add 1 to the expanded expression:
\[
3x^2 - 12x + 12 + 1 = 3x^2 - 12x + 13
\]
4. Set the equation equal to 28:
\[
3x^2 - 12x + 13 = 28
\]
5. Subtract 28 from both sides to convert into standard form:
\[
3x^2 - 12x + 13 - 28 = 0
\]
\[
3x^2 - 12x - 15 = 0
\]
**Standard Form:**
The standard form of the quadratic is:
\[ 3x^2 - 12x - 15 = 0 \]
**Coefficients:**
- \(a = 3\)
- \(b = -12\)
- \(c = -15\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F532d2df1-6bef-42be-bbaa-e1703c54e78f%2F1db5b362-9e63-46b2-9a06-91f9f6a3ae7d%2Fs32hmwb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Convert this into a quadratic in standard form. State a, b, and c for your solution.
\[ 3(x - 2)^2 + 1 = 28 \]
**Answer:**
Begin by expanding the expression on the left-hand side:
1. Expand \((x - 2)^2\):
\[
(x - 2)^2 = x^2 - 4x + 4
\]
2. Multiply the entire expression by 3:
\[
3(x^2 - 4x + 4) = 3x^2 - 12x + 12
\]
3. Add 1 to the expanded expression:
\[
3x^2 - 12x + 12 + 1 = 3x^2 - 12x + 13
\]
4. Set the equation equal to 28:
\[
3x^2 - 12x + 13 = 28
\]
5. Subtract 28 from both sides to convert into standard form:
\[
3x^2 - 12x + 13 - 28 = 0
\]
\[
3x^2 - 12x - 15 = 0
\]
**Standard Form:**
The standard form of the quadratic is:
\[ 3x^2 - 12x - 15 = 0 \]
**Coefficients:**
- \(a = 3\)
- \(b = -12\)
- \(c = -15\)
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