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Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4.

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Presentation on theme: "Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4."— Presentation transcript:

1 Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x m 2 – 10m + 25 (m – 5) 2 Factor

2 Solving Quadratic Equations by Completing the Square Do you remember…. What are the properties of a square? Standard: 14.0

3 CONCEPT TASK

4 x x A = x 2 x 1 1 x2x2 x COPY ME!!!

5 Represent the Expression: x 2 + 3x + 6

6 CONCEPT TASK x 2 + 4x + 4 2x 2 + 3x – 4 – 3x 2 + 3x – 4 WORK WITH YOUR PARTNERS

7 CONCEPT TASK x 2 + 4x + 4

8 CONCEPT TASK 2x 2 + 3x – 4

9 CONCEPT TASK 2x 2 + 3x – 4

10 CONCEPT TASK – 2x 2 – 3x + 4

11 CONCEPT TASK – 2x 2 – 3x + 4

12 CONCEPT TASK Using ONLY the Algebra tiles below, create a square.

13 CONCEPT TASK What do you do to complete the square x 2 + 2x + ___

14 CONCEPT TASK How many 1-unit tiles do you need to add to complete the square? x 2 + 2x + ____

15 CONCEPT TASK How many 1-unit tiles do you need to add to complete the square? x 2 + 2x + ____ 1

16 CONCEPT TASK How many 1-unit tiles do you need to add to complete the square? x 2 + 2x + ____ 1 x + 1

17 Completing the Square Expression Number of 1-tiles needed to be added to complete the square What is the Area of your Square? A. x 2 + 2x + ? (x + ____ ) 2 B. x 2 + 4x + ? C. x 2 – 6x + ? D. x 2 + 8x + ?

18 CONCEPT TASK What do you do to complete the square x 2 + 4x + ___

19 CONCEPT TASK What do you do to complete the square x 2 + 8x + ___

20 CONCEPT TASK What do you do to complete the square x 2 – 6x + ______

21 CONCEPT TASK Now arrange your tiles to make a perfect square

22 CONCEPT TASK How many 1-unit tiles do you need to add to complete the square? x 2 - 6x + ______ 9

23 CONCEPT TASK x - 3

24 CONCEPT TASK x - 3 Area= l w A = (x-3)(x-3) A=(x - 3) 2

25 CONCEPT TASK x 2 - 6x + 9 = (x - 3) 2

26 Completing the Square Expression Number of 1-tiles needed to be added to complete the square What is the Area of your Square? A. x 2 + 2x + ? 1(x + 1 ) 2 B. x 2 + 4x + ? 4 (x + 2) 2 C. x 2 – 6x + ? 9 (x – 3) 2 D. x 2 + 8x + ? 16 (x + 4) 2 What is the relationship between the values in Column 2 and 3 and the coefficient of the linear term? What were the steps you took in order to complete the square? THINK PAIR SHARE

27

28 Lets try without algebra tiles Find the missing value. s 2 -16s + _ Step 1: Divide b by 2 Step 2: Square the result of step 1 Step 3: Add the result to the original expression Step 4: Factor (x + ) 2 (-8 2 ) = 64 s 2 -16s + 64

29 COMPLETE THE SQUARE x x + ___= (x + ___ ) 2 x 2 – 16x + ___= (x – ___ ) 2 x x + ___= (x + ___ ) 2

30 COMPLETE THE SQUARE x 2 + 5x + ___= (x + ___ ) 2 g g + ___= p 2 – 9p + ___=

31 COMPLETE THE SQUARE m 2 – 1.8m + ___= (x – ___ ) 2

32 CONCEPT TASK JOURNAL: Your best friend was absent today. Write your friend a letter explaining how to complete the square using algebra tiles and how to do it without using algebra tiles

33 COMPLETE THE SQUARE Daily Practice Skills Practice Pg Pg 735 Lesson

34 Dispatch Tuesday 2/26/13 Find the value of c that makes the trinomial a perfect square. (Use Algebra Tiles and solve Algebraically) 1. x 2 – 10x + c

35 VISUALLY x - 5 Area= l w A = (x-5)(x-5) A=(x - 5) 2

36 Find the missing value. x 2 –10x + _____ Step 1: Divide b by 2 Step 2: Square the result of step 1 Step 3: Add the result to the original expression Step 4: Factor (x + ) 2 (– 5 2 ) = 25 x 2 – 10x + 25 (x – 5) 2 ALGEBRAICALLY

37 Dispatch Thursday 2/28/13 Solve the Equation. 1. x 2 – 2x + 1 = 25 x = – 4 and m 2 – 8m + 16 (m – 4) 2 Factor Find the value of c that makes the trinomial a perfect square. 3. x 2 + 8x + c

38 Solving Quadratic Equations by Completing the Square Do you remember…. What are the other methods for solving quadratic equations? Standard: 14.0

39 CONCEPT TASK

40 x x A = x 2 x 1 1 x2x2 x

41 1. x – 5 = 2 x – 5 = 2

42 1. x – 5 = 2 x – 5 = 2

43 1. x – 5 = 2 x – 5 = 2

44 1. x – 5 = 2 x = 7

45 YOUR TURN 1. x + 6 = – x – 4 = – 8 3. x 2 + 4x = 2

46 1. x + 6 = – 4 x = – 2

47 1. 2x – 4 = – 8 x = 4

48 x 2 + 4x = 5

49

50 x + 2

51 x 2 + 4x + 4 = 9 (x + 2) 2 = 9

52 Step 2: Take the square root of each side to cancel the square. Step 3: Solve One-Step Equation. (m + 2) 2 = 9 Step 4: Split Up (x + 2) 2 = 9

53 m= – m= – 2 – 3 m= 1 m= – 5 Challenge: Is there a faster method to complete the square without using Algebra Tiles? Write in complete sentences Think Pair Share

54 YOUR TURN Solve the equation using completing the square. Represent your answer both Visually with Algebra Tiles and Algebraically. x 2 + 6x = 2 q 2 – 2q = 16

55 1. x 2 + 4x + 3 = 0

56 x 2 + 4x + 3 = 0

57

58

59

60 (x + 2) 2 = 1

61 Step 2: Take the square root of each side to cancel the square. Step 3: Solve One-Step Equation. (x + 2) 2 = 1 Step 4: Split Up (x + 2) 2 = 1

62 x= – x= – x= -1 x= – 3 Think Pair Share

63 YOUR TURN x 2 – 4x – 5 = 0 x 2 – 14x + 30 = 6 x x + 49 = 10

64 Daily Practice I want you to create your own Completing the Square Problem. Make sure you represent it using Algebra Tiles and algebraically. Make a key and be ready to share the problem with your partners tomorrow. Study Guide and Intervention Pg 118 #1-18 ODD (Skip 11)


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