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When completing the square, what value should replace the '?' x + 4x +3 (x+ ? )² – 1 - O 1 O 5 8

When completing the square, what value should replace the '?' x + 4x +3 (x+ ? )² – 1 - O 1 O 5 8

Algebra and Trigonometry (6th Edition)
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 **Question:** When completing the square, what value should replace the '?'? \[ x^2 + 4x + 3 \] \[ (x + ?)^2 - 1 \] **Options:** - 1 - 5 - 2 - 8 --- **Explanation for Students:** In this problem, you are asked to complete the square for the quadratic expression \( x^2 + 4x + 3 \) and determine which value should replace the '?' in the equation \((x + ?)^2 - 1\). --- ### Completing the Square Process 1. **Start with the quadratic expression:** \[ x^2 + 4x + 3 \] 2. **Rewrite the expression without the constant term:** \[ x^2 + 4x \] 3. **Take half of the coefficient of the linear term (4), square it, and add and subtract this square:** \[ \left( \frac{4}{2} \right)^2 = 2^2 = 4 \] \[ x^2 + 4x + 4 - 4 + 3 \] 4. **Group the perfect square trinomial and the constant terms:** \[ (x + 2)^2 - 4 + 3 \] 5. **Combine the constant terms:** \[ (x + 2)^2 - 1 \] Thus, the quadratic expression \( x^2 + 4x + 3 \) rewritten in completed square form is: \[ (x + 2)^2 - 1 \] So, the value that should replace the '?' is \( 2 \). **Therefore, the correct answer is \( 2 \).** This detailed process helps you understand the steps required to complete the square for a given quadratic expression. Make sure to practice more problems to gain confidence in completing the square!
Transcribed Image Text:### Completing the Square **Question:** When completing the square, what value should replace the '?'? \[ x^2 + 4x + 3 \] \[ (x + ?)^2 - 1 \] **Options:** - 1 - 5 - 2 - 8 --- **Explanation for Students:** In this problem, you are asked to complete the square for the quadratic expression \( x^2 + 4x + 3 \) and determine which value should replace the '?' in the equation \((x + ?)^2 - 1\). --- ### Completing the Square Process 1. **Start with the quadratic expression:** \[ x^2 + 4x + 3 \] 2. **Rewrite the expression without the constant term:** \[ x^2 + 4x \] 3. **Take half of the coefficient of the linear term (4), square it, and add and subtract this square:** \[ \left( \frac{4}{2} \right)^2 = 2^2 = 4 \] \[ x^2 + 4x + 4 - 4 + 3 \] 4. **Group the perfect square trinomial and the constant terms:** \[ (x + 2)^2 - 4 + 3 \] 5. **Combine the constant terms:** \[ (x + 2)^2 - 1 \] Thus, the quadratic expression \( x^2 + 4x + 3 \) rewritten in completed square form is: \[ (x + 2)^2 - 1 \] So, the value that should replace the '?' is \( 2 \). **Therefore, the correct answer is \( 2 \).** This detailed process helps you understand the steps required to complete the square for a given quadratic expression. Make sure to practice more problems to gain confidence in completing the square!
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