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

2. Completing the Square

3. Today’s Objective
Today, you’ll learn how to solve equations by completing the square.

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

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

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

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

8. Example 1: Solve by Completing the Square
Solve x2 – 12x + 5 = 0.
First: x2 – 12x + ____ = -5

9. Example 2: Solve by Completing the Square
Solve x2 – 8x + 36 = 0.

10. Example 3: Solve by Completing the Square
Solve 5x2 = 6x + 8.

11. Vertex Form

12. Standard form vertex

13. Vertex: highest or lowest
point on the graph.
2 ways to find Vertex:
1) Calculator:
2nd  CALC
MIN or MAX
2) Algebraically

14. Find the Vertex
x2 + 8x + 1
x2 + 2x – 5
2x2 – 10x + 3

15. Complete the Square Investigation
Step 1: Complete the square: X2 + 4x – 4 = 0 Step 2: DON’T SOLVE! Instead get zero on one side. Step 3: graph the non-zero side and find the vertex

16. Completing the Square Finds the vertex!
Use completing the square to find the vertex of each:
x2 + 6x + 8 = 0
X2 – 2x + 10 = 0

17. Vertex Form
Lucky for us, we can use a calculator to find the vertex instead of completing the square!

18. Converting from Standard to Vertex
Standard: y = ax2 + bx + c Things you will need: a = and Vertex: Vertex: y = a(x – h)2 + k

19. Example
Convert from standard form to vertex form.
y = -3x2 + 12x + 5

20. Example
Convert from standard form to vertex form.
y = x2 + 2x + 5

21. Now Convert and Solve
Convert each quadratic from standard to vertex form. Then Solve for x.
x2 + 6x – 5 = 0

22. Now Convert and Solve
Convert each quadratic from standard to vertex form.
3x2 – 12x + 7 = 0
-2x2 + 4x – 3 = 0