1. Warm Up
Solve by factoring. x2 + 10x + 25 x2 – 16x + 64 x2 + 18x + 81

2. Completing the Square

3. Perfect Square Trinomials
Quadratic Trinomials with a repeated factor! x2 + 10x + 25 x2 – 16x + 64 x2 + 18x + 81

4. Solving a Perfect Square Trinomial
We can solve a Perfect Square Trinomial using square roots.
x2 + 10x + 25 = 36

5. Solving a Perfect Square Trinomial
x2 – 14x + 49 = 81

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

7. Solving by Completing the Square
Solve by completing the square: x2 + 6x + 8 = 0

8. Solving by Completing the Square
Solve by completing the square: x2 – 12x + 5 = 0

9. Solving by Completing the Square
Solve by completing the square: x2 – 8x + 36 = 0

10. Vertex Form

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

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

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

14. Vertex Form

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

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

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

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

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