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### Presentation1

1. 1. Completing the Square<br />
2. 2. Practice factoring the following using the algebra tiles above: <br />x2+ 5x + 6<br />x2+ 4x + 4<br />x2+ 6x + 9<br />x2+ 8x + 16<br />click on to check your work…<br />
3. 3. #1) x2+ 5x + 6<br />
4. 4. #1) x2+ 5x + 6<br />
5. 5. #1) x2+ 5x + 6<br />(x + 3) (x + 2) <br />
6. 6. x2 + 4x + 4<br />
7. 7. #2) x2+ 4x + 4<br />
8. 8. #2) x2+ 4x + 4<br />(x + 2)(x + 2) = (x + 2)2<br />
9. 9. #3) x2+ 6x + 9<br />
10. 10. #3) x2+ 6x + 9<br />
11. 11. #3) x2+ 6x + 9<br />(x + 3)(x + 3) = (x + 3)2<br />
12. 12. #4) x2+ 8x + 16<br />
13. 13. #4) x2+ 8x + 16<br />
14. 14. #4) x2+ 8x + 16<br />(x + 4)(x + 4) = (x + 4)2<br />
15. 15. What do #2, 3 & 4 have in common when you built them?  <br />
16. 16. What do #2, 3 & 4 have in common when you built them?  <br />They all made squares!!!<br />
17. 17. Try factoring 4x2+ 8x + 4.  What do you notice?<br />
18. 18. Try factoring 4x2+ 8x + 4.  What do you notice?<br />
19. 19. Try factoring 4x2+ 8x + 4.  What do you notice?<br />It’s still a square!!<br />(2x + 2)2<br />
20. 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.  <br />
21. 21. Solve each of the following equations:A.  x2+ 4x + 1 = 0 B.  (x + 2)2= 3<br />
22. 22. Solve each of the following equations:A.  x2+ 4x + 1 = 0 B.  (x + 2)2= 3<br />
23. 23. Solve each of the following equations:A.  x2+ 4x + 1 = 0 B.  (x + 2)2= 3<br />You ended up getting the same answer!<br />
24. 24. Which method do you think was more straight forward? A or B?<br />
25. 25. Build a square (the best you can) to factor x2 + 4x + 1 <br />
26. 26. Build a square (the best you can) to factor x2 + 4x + 1 <br />
27. 27. What do you need to “add” to complete your square?<br />
28. 28. You needed to borrow 3 tiles… <br />
29. 29. How will you write this algebraically?<br />
30. 30. x2+ 4x + 1 + 3 – 3x2 + 4x + 4– 3<br />
31. 31. How will you now write this in “factored” form?<br />x2 + 4x + 4 – 3<br />
32. 32. How will you now write this in “factored” form?<br />x2 + 4x + 4 – 3 =<br />(x +2)2 - 3<br />
33. 33. Practice completing the square on the following expressions:<br />x2 + 6x + 5<br />x2 + 8x + 5<br />4x2+ 8x + 1<br />
34. 34. Practice completing the square on the following expressions:<br />x2 + 6x + 5 = x2 + 6x + 5 + 4 - 4<br />x2 + 8x + 5 <br />4x2+ 8x + 1<br />
35. 35. Practice completing the square on the following expressions:<br />x2 + 6x + 5 = x2 + 6x + 5 + 4 – 4<br /> = (x + 3)2 - 4<br />x2 + 8x + 5 <br />4x2+ 8x + 1<br />
36. 36. Practice completing the square on the following expressions:<br />x2 + 6x + 5 = (x + 3)2 - 4<br />x2 + 8x + 5 <br />4x2+ 8x + 1<br />
37. 37. Practice completing the square on the following expressions:<br />x2 + 6x + 5 = (x + 3)2 - 4<br />x2 + 8x + 5 = x2 + 8x + 5 + 11 - 11<br />4x2+ 8x + 1<br />
38. 38. Practice completing the square on the following expressions:<br />x2 + 6x + 5 = (x + 3)2 - 4<br />x2 + 8x + 5 = x2 + 8x + 5 + 11 – 11<br /> = (x + 4)2 - 11<br />4x2+ 8x + 1<br />
39. 39. Practice completing the square on the following expressions:<br />x2 + 6x + 5 = (x + 3)2 - 4<br />x2 + 8x + 5 = (x + 4)2 - 11<br />4x2+ 8x + 1<br />
40. 40. Practice completing the square on the following expressions:<br />x2 + 6x + 5 = (x + 3)2 - 4<br />x2 + 8x + 5 = (x + 4)2 - 11<br />4x2+ 8x + 1 = 4x2 + 4x + 1 + 1 – 1<br />
41. 41. Practice completing the square on the following expressions:<br />x2 + 6x + 5 = (x + 3)2 - 4<br />x2 + 8x + 5 = (x + 4)2 - 11<br />4x2+ 8x + 1 = 4x2 + 4x + 1 + 1 – 1<br /> = (2x + 2)2 – 1<br />
42. 42. Practice completing the square on the following expressions:<br />x2 + 6x + 5 = (x + 3)2 - 4<br />x2 + 8x + 5 = (x + 4)2 - 11<br />4x2+ 8x + 1 = (2x + 2)2 – 1<br />
43. 43. Practice completing the square on the following expressions:<br />x2 + 6x + 5 = (x + 3)2 - 4<br />x2 + 8x + 5 = (x + 4)2 - 11<br />4x2+ 8x + 1 = (2x + 2)2 – 1<br />
44. 44. What did you notice about all the problems in this lesson?<br />
45. 45. What did you notice about all the problems in this lesson?<br />Everything was positive.<br />
46. 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!<br />