1. + Completing the Square and Vertex Form

2. + Completing the Square

3. + Perfect Square Trinomials Quadratic Trinomials with a repeated factor! X 2 + 10x + 25 X 2 – 16x + 64 X 2 + 18x + 81

4. + Solving a Perfect Square Trinomial We can solve a Perfect Square Trinomial using square roots. X 2 + 10x + 25 = 36

5. + Solving a Perfect Square Trinomial X 2 – 14x + 49 = 81

6. + What if it’s not a Perfect Square Trinomials?! If an equation is NOT a perfect square Trinomial, we can use a method called COMPLETING THE SQUARE.

7. + Completing the Square Using the formula for completing the square, turn each trinomial into a perfect square trinomial.

8. + Solving by Competing the Square Solve by completing the square: X 2 + 6x + 8 = 0

9. + Solving by Competing the Square Solve by completing the square: X 2 – 12x + 5 = 0

10. + Solving by Competing the Square Solve by completing the square: X 2 – 8x + 36 = 0

11. + Vertex Form

12. + Standard form vertex

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

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

15. + Complete the Square Investigation Step 1: Complete the square: X 2 + 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: 1) x 2 + 6x + 8 = 0 2) X 2 – 2x + 10 = 0

17. + Vertex Form

18. + Converting from Standard to Vertex Standard: y = ax 2 + 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 = -3x 2 + 12x + 5

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

21. + Now Convert and Solve Convert each quadratic from standard to vertex form. Then Solve for x. 1. x 2 + 6x – 5 = 0

22. + Now Convert and Solve Convert each quadratic from standard to vertex form. 1. 3x 2 – 12x + 7 = 0 2. -2x 2 + 4x – 3 = 0