# Completing the Square

Videos to help Algebra I students learn how to rewrite quadratic expressions given in standard form, ax2 + bx + c, in the equivalent completed-square form, a(x-h)2 + k, and recognize cases for which factored or completed-square form is most efficient to use.

New York State Common Core Math Module 4, Algebra I, Lesson 11, Lesson 12

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Common Core For Algebra I

Lesson 11 Summary

Just as factoring a quadratic expression can be useful for solving a quadratic equation, completing the square also provides a form that facilitates solving a quadratic equation.

Lesson 11 Opening Exercise:

In lesson 11, we will look at completing the square for expressions where the leading coefficient a = 1.

Rewrite the following perfect square quadratic expressions in standard form.
(x + 10)2
(x + 6)2

Example 1
Rewrite the following standard form quadratic expressions as perfect squares.
x2 - 8x + 16
x2 + 12x + 36

Example 2
Find an expression equivalent to x2 + 10x + 36 that includes a perfect square binomial.

Complete the Square Steps:
1. Isolate the x's on one side
2. Half the linear coefficient
3. Square this value
4. Add this value to both sides
5. Rewrite new quadratic as a binomial squared

Rewrite the following expressions by completing the square
x2 - 3x + 10
x2 + 8x + 3

Lesson 12

In lesson 12, we will look at completing the square for expressions where the leading coefficient a ≠ 1.

We will need to modify the steps from Lesson 11

Complete the Square Steps:
1. Isolate the x's on one side
2. Factor out the leading coefficient
3. Half the linear coefficient
4. Square this value
5. Add this value to both sides
6. Rewrite new quadratic as a binomial squared

Rewrite each expression by completing the square.
2x2 + 16x + 3
3x2 + 12x - 8
4p2 - 12p +13

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