1. Warm-Up
Factor the following trinomials.
What do you notice?
1. x2 - 6x x2 - 4x + 1

2. Completing the Square

3. Think-Pair-Share
Have students solve the following equations individually, share their solutions and methods with their partners, and then discuss the solutions with the entire class.
1. x2 = 9
2. (x+1)2 = 9
3. (x+1)2 -5 = 4
The class should discuss how their methods for each problem differed. In addition, students should recognize that all answers are to include and why.

4. Today’s Objectives Today, you’ll learn how to:
Solve equations by completing the square.
Rewrite functions by completing the square.
Today, you’ll learn how to:

5. Perfect Square Trinomials
1) x2 – 8x + ____ ) x2 + 16x + ____
x2 + 7x + ____ ) x2 – 13x + ____

6. Can you write a formula that will work for every example?
1) x2 – 8x + ____ ) x2 + 16x + ____
x2 + 7x + ____ ) x2 – 13x + ____

7. This will always result in a perfect square trinomial!
Introducing…
the magic number!
This will always result in a perfect square trinomial!

8. Adding the magic number,
to both sides of a quadratic equation is called completing the square.

9. Example 3: Solve by Completing the Square
Solve x2 – 12x + 5 = 0.
First: x2 – 12x + ____ = -5

10. Example 4: Solve by Completing the Square
Solve x2 – 8x + 36 = 0.

11. Example 5: Solve by Completing the Square
Solve x2 + 22x + 21 = 0.

12. Example 6: Solve by Completing the Square
Solve 5x2 = 6x + 8.