1. Completing the Square

2. Practice factoring the following using the algebra tiles above: x2+ 5x + 6 x2+ 4x + 4 x2+ 6x + 9 x2+ 8x + 16 click on to check your work…

3. #1) x2+ 5x + 6

4. #1) x2+ 5x + 6

5. #1) x2+ 5x + 6 (x + 3) (x + 2)

6. x2 + 4x + 4

7. #2) x2+ 4x + 4

8. #2) x2+ 4x + 4 (x + 2)(x + 2) = (x + 2)2

9. #3) x2+ 6x + 9

10. #3) x2+ 6x + 9

11. #3) x2+ 6x + 9 (x + 3)(x + 3) = (x + 3)2

12. #4) x2+ 8x + 16

13. #4) x2+ 8x + 16

14. #4) x2+ 8x + 16 (x + 4)(x + 4) = (x + 4)2

15. What do #2, 3 & 4 have in common when you built them?

16. What do #2, 3 & 4 have in common when you built them? They all made squares!!!

17. Try factoring 4x2+ 8x + 4. What do you notice?

18. Try factoring 4x2+ 8x + 4. What do you notice?

19. Try factoring 4x2+ 8x + 4. What do you notice? It’s still a square!! (2x + 2)2

20. All of the above examples are considered perfect square trinomials. Being able to rewrite a trinomial in "perfect square" form allows you to solve for it using the square root method instead of the quadratic formula.

21. Solve each of the following equations:A. x2+ 4x + 1 = 0 B. (x + 2)2= 3

22. Solve each of the following equations:A. x2+ 4x + 1 = 0 B. (x + 2)2= 3

23. Solve each of the following equations:A. x2+ 4x + 1 = 0 B. (x + 2)2= 3 You ended up getting the same answer!

24. Which method do you think was more straight forward? A or B?

25. Build a square (the best you can) to factor x2 + 4x + 1

26. Build a square (the best you can) to factor x2 + 4x + 1

27. What do you need to “add” to complete your square?

28. You needed to borrow 3 tiles…

29. How will you write this algebraically?

30. x2+ 4x + 1 + 3 – 3x2 + 4x + 4– 3

31. How will you now write this in “factored” form? x2 + 4x + 4 – 3

32. How will you now write this in “factored” form? x2 + 4x + 4 – 3 = (x +2)2 - 3

33. Practice completing the square on the following expressions: x2 + 6x + 5 x2 + 8x + 5 4x2+ 8x + 1

34. Practice completing the square on the following expressions: x2 + 6x + 5 = x2 + 6x + 5 + 4 - 4 x2 + 8x + 5 4x2+ 8x + 1

35. Practice completing the square on the following expressions: x2 + 6x + 5 = x2 + 6x + 5 + 4 – 4 = (x + 3)2 - 4 x2 + 8x + 5 4x2+ 8x + 1

36. Practice completing the square on the following expressions: x2 + 6x + 5 = (x + 3)2 - 4 x2 + 8x + 5 4x2+ 8x + 1

37. Practice completing the square on the following expressions: x2 + 6x + 5 = (x + 3)2 - 4 x2 + 8x + 5 = x2 + 8x + 5 + 11 - 11 4x2+ 8x + 1

38. Practice completing the square on the following expressions: x2 + 6x + 5 = (x + 3)2 - 4 x2 + 8x + 5 = x2 + 8x + 5 + 11 – 11 = (x + 4)2 - 11 4x2+ 8x + 1

39. Practice completing the square on the following expressions: x2 + 6x + 5 = (x + 3)2 - 4 x2 + 8x + 5 = (x + 4)2 - 11 4x2+ 8x + 1

40. Practice completing the square on the following expressions: x2 + 6x + 5 = (x + 3)2 - 4 x2 + 8x + 5 = (x + 4)2 - 11 4x2+ 8x + 1 = 4x2 + 4x + 1 + 1 – 1

41. Practice completing the square on the following expressions: x2 + 6x + 5 = (x + 3)2 - 4 x2 + 8x + 5 = (x + 4)2 - 11 4x2+ 8x + 1 = 4x2 + 4x + 1 + 1 – 1 = (2x + 2)2 – 1

42. Practice completing the square on the following expressions: x2 + 6x + 5 = (x + 3)2 - 4 x2 + 8x + 5 = (x + 4)2 - 11 4x2+ 8x + 1 = (2x + 2)2 – 1

43. Practice completing the square on the following expressions: x2 + 6x + 5 = (x + 3)2 - 4 x2 + 8x + 5 = (x + 4)2 - 11 4x2+ 8x + 1 = (2x + 2)2 – 1

44. What did you notice about all the problems in this lesson?

45. What did you notice about all the problems in this lesson? Everything was positive.

46. On the wall wisher below, how would this process change when given negative values in your expression? Be sure to put your name on your note to get credit!