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Chapter 10 Lesson 10-5 This stAIR is designed for Ms. Goghar’s Grade 9 Algebra 1 class. You are expected to follow directions on each slide and navigate.

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Presentation on theme: "Chapter 10 Lesson 10-5 This stAIR is designed for Ms. Goghar’s Grade 9 Algebra 1 class. You are expected to follow directions on each slide and navigate."— Presentation transcript:

1

2 Chapter 10 Lesson 10-5

3 This stAIR is designed for Ms. Goghar’s Grade 9 Algebra 1 class. You are expected to follow directions on each slide and navigate through this powerpoint carefully. Your goal is to understand the concept of solving quadratic equations and its relation to the roots (zeros) of quadratic functions and to learn how to solve quadratic equations by factoring.

4 To master the skill of solving quadratic equations by factoring

5 Pencil, Paper, and eraser TI-84 (optional)

6

7 Solve this equation for n: What does n equal? 2 2

8

9 First, you should subtract 6 from both sides. Now, what should the next step be? What does n equal? 2 2

10 First, you should subtract 6 from both sides. Now you need to divide both sides by 4. What does n equal? 2 2

11 First, you should subtract 6 from both sides Then, divide both sides by 4 What does n equal? 2 2

12 Solve for a: What does a equal? 104 -40

13 Solve for a:

14 NOW: Solve for a: Step 1: Add 9 on both sides So, Think: What is the 2 nd Step you need to do to solve for a? What does a equal? 104 -40

15 Solve for a: Step 1: Add 9 on both sides Step 2: Multiply 8 to both sides What does a equal? 104 -40

16 Factor the expression completely: What is the Complete Factored form?

17 Factor the expression:

18 Factor the expression completely: Step 1: Factor out the GCF. In this case, GCF = 2. Step 2: You need to factor Note: Factoring Difference of Perfect Squares: What is the Complete Factored form?

19 Factor the expression completely: Step 1: Factor out the GCF. In this case, GCF = 2. Step 2: Factor So now, what is the Complete Factored form?

20 Factor the expression: Is it: OR

21 Factor the expression: This expression cannot be factored. Therefore, it is

22 Notes: Steps to Factor Polynomials: I Un-DISTRIBUTE GCF II Un-FOIL a 2 - b 2 III Un-FOIL ax 2 + bx + c IV Polynomials that cannot be factored are PRIME Hint: Is it possible to factor the given expression? Does it follow any of the factoring rules listed above? Back to Lesson Warm-Up #4

23 Factor the expression completely: What is the expression in factored form?

24 Factor the expression completely: Expression in Factored Form:

25 Study the Notes Below: Steps to Factor Polynomials: I Un-DISTRIBUTE GCF II Un-FOIL a 2 - b 2 III Un-FOIL ax 2 + bx + c IV Polynomials that cannot be factored are PRIME Factor completely:

26 Factor the expression completely: Step 1: (2c+___)(c+___) You need to think of factors of 14 that will work. Possibilities: 1 and 14; 2 and 7 Remember to check for the middle term when you FOIL. What is the expression in factored form?

27 Factor the expression completely: What is the expression in factored form?

28 Factor the expression:

29 Study the Notes Below: Steps to Factor Polynomials: I Un-DISTRIBUTE GCF II Un-FOIL a 2 - b 2 III Un-FOIL ax 2 + bx + c IV Polynomials that cannot be factored are PRIME Factor completely:

30 Factor the expression completely: Step 1: (3p+___)(p+___) Think: What Factors of 20 will give you the correct middle term? What is the expression in factored form?

31

32 For every real number a and b, if ab = 0, then a = 0 or b = 0. Example: If, then x + 2 = 0 or x + 3 = 0

33 If x = 0, then You have 5 seconds to think before the answer appears…

34 If y = 0, then You have 5 seconds to think before the answer appears…

35 Study the Example Question carefully and think about how you may want to solve it The worked out solution(s) and the final answer of the example will appear after a few seconds Study every step of the solution and the answer carefully so you will be able to solve similar problems later on When you are ready to continue, navigate to the next slide.

36 Study the “You Try” Question carefully and think about how you may want to solve it Solve the problem on the paper that you have with you The worked out solution(s) and the final answer of the problem will appear after 10-15 seconds Check your work (step-by-step) with the worked out solution and final answer If you made mistakes in solving the problem on your paper, you should correct them When you are ready to continue, navigate to the next slide.

37 Using the Zero-Product Property, Solve:

38 Check your Solutions:

39 Using the Zero-Product Property, Solve :

40

41

42 Solve : A.A. A.A. B. C.

43 Solve :

44 Back to Examples

45 Solve by Factoring :

46

47 Solve : A.A. A.A. B. C.

48 Solve :

49 Back to Examples

50 Solve by Factoring :

51

52 Solve : A.A. A.A. B. C.

53 Solve :

54 Back to Examples

55 Let x = width of a side of the box So, Width of material = x + 3 + 3 = x + 6 Length of material = x + 2 + 3 + 3 Length = x + 8

56 Length x Width = Area of Sheet

57

58 NOTES: What is the connection between solving quadratic equations by graphing and by factoring? FactoringGraphing

59 If the roots of the quadratic function g(x) are -2 and 2, what are the solutions of the equation: g(x) = 0

60 If the solution of the quadratic equation h(x) are -3 and -5, what are the zeros of the function: y = h(x)

61 Solve :

62 Solve by Factoring :

63

64 1. Solve : A.A. A.A. B. C.

65 Back to QUIZ Back to QUIZ Using the Zero-Product Property, Solve:

66 NOW TRY QUESTION 2

67 2. Solve by Factoring : A.A. A.A. B. C.

68 Solve by Factoring: Back to QUIZ Back to QUIZ

69 NOW TRY QUESTION 3

70 3. Solve by Factoring : A.A. A.A. B. C.

71 Solve by Factoring: Back to QUIZ Back to QUIZ

72 NOW TRY QUESTION 4

73 4. Solve by Factoring : A.A. A.A. B. C.

74 Solve: Back to QUIZ Back to QUIZ

75 Please click Home to return to the First Slide to allow other students to work on this.


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