# Mastering Completing the Square

Mastering Completing the Square
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Slide 1: Slide

This lesson contains 17 slides, with interactive quizzes and text slides.

Lesson duration is: 30 min

## Items in this lesson

Mastering Completing the Square

#### Slide 1 -Slide

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Learning Objective
Understand how to complete the square and apply it to solve quadratic equations.

#### Slide 2 -Slide

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What is Completing the Square?
Completing the square is a method used to solve quadratic equations by creating a perfect square trinomial.

#### Slide 3 -Slide

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Step 1: Write the Equation
Start with a quadratic equation in the form ax^2 + bx + c = 0. Make sure the coefficient of x^2 is 1. If the coefficient of x^2 is not 1 factor it out.

#### Slide 4 -Slide

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Step 2: Rewrite the Expression
Step 2. Rewrite the Expression
ax^2 + bx + c
=a(x^2+b/a x)+c

#### Slide 5 -Slide

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Step 3: Add AND Subtract (b/2a)^2
Add and subtract (b/2a)^2 to the equation to create a perfect square trinomial.
=a(x^2+b/a x)+c
=a(x^2+b/a x+(b/2a)^2-(b/2a)^2)+c

#### Slide 6 -Slide

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Step 4: Simplify
Write the perfect square trinomial as a squared binomial and solve for x.
=a(x^2+b/a x+(b/2a)^2-(b/2a)^2)+c
=a((x+b/2a)^2-(b/2a)^2)+c

#### Slide 7 -Slide

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Step 5: Write in Vertex Form
Write the perfect square trinomial as a squared binomial and solve for x.
=a((x+b/2a)^2-(b/2a)^2)+c
=a((x+b/2a)^2-b/4a+c

#### Slide 8 -Slide

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Example Problem
Given the equation x^2 + 6x +8 , demonstrate step-by-step how to complete the square and solve for x.
Step 2: Plug in the given information from the equation above A=1      B=6      C=8
=a(x^2+b/a x)+c
=1(x^2+6/1 x)+8

#### Slide 9 -Slide

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Example Problem
Given the equation x^2 + 6x +8 , demonstrate step-by-step how to complete the square and solve for x.
Step 3: Add AND Subtract  (b/2a)^2 using the information given.
(b/2a)^2=(6/2(1))^2=9
=1(x^2+6x+9-9)+8

#### Slide 10 -Slide

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Example Problem
Given the equation x^2 + 6x +8 , demonstrate step-by-step how to complete the square and solve for x.
Step 4: Simplify by the finding the factors of (x^2+6x+9) using the box method .
=1(x^2+6x+9-9)+8
=1((x+3)^2-9)+8

#### Slide 11 -Slide

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Example Problem
Given the equation x^2 + 6x +8 , demonstrate step-by-step how to complete the square and solve for x.
Step 5: Write in Vertex Form.
=1((x+3)^2-9)+8 <- Distribute the 1
=(x+3)^2-9+8 <-Combine like terms

#### Slide 12 -Slide

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Practice Problem
Solve the equation x^2 - 8x + 12  using the completing the square method.

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Summary
Completing the square is a powerful method for solving quadratic equations and understanding it is essential for success in Algebra 2.

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Write down 3 things you learned in this lesson.

#### Slide 15 -Open question

Have students enter three things they learned in this lesson. With this they can indicate their own learning efficiency of this lesson.
Write down 2 things you want to know more about.

#### Slide 16 -Open question

Here, students enter two things they would like to know more about. This not only increases involvement, but also gives them more ownership.
Ask 1 question about something you haven't quite understood yet.

#### Slide 17 -Open question

The students indicate here (in question form) with which part of the material they still have difficulty. For the teacher, this not only provides insight into the extent to which the students understand/master the material, but also a good starting point for the next lesson.