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Math 20: Foundations FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q, including: vertex.

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Presentation on theme: "Math 20: Foundations FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q, including: vertex."— Presentation transcript:

1 Math 20: Foundations FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q, including: vertex intercepts domain and range axis of symmetry. F. Everything Quadratics

2 Getting Started String Art p.356

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6 What DO YOU Think? P.357

7 1. What is a Quadratic? FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q, including: vertex intercepts domain and range axis of symmetry.

8 1. What is a Quadratic?

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10 Summary p.359

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12 Practice Ex. 7.1 (p.360) #1-6

13 2. Properties of Quadratic Graphs FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q, including: vertex intercepts domain and range axis of symmetry.

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15 Reflections p.362

16 Vertex - The point at which the quadratic function reaches its maximum or minimum value. Axis of Symmetry - A line that separates a 2-D figure into two identical parts. For example, a parabola has a vertical axis of symmetry passing through its vertex.

17 Example 1

18 Example 2

19 Does this last Function have a max or min value?

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21 Example 3

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23 Summary p.368

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26 Practice Ex. 7.2 (p.368) #1-16 #4-19

27 3. Graphing to Solve Quadratic Equations FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q, including: vertex intercepts domain and range axis of symmetry.

28 3. Graphing to Solve Quadratic Equations A zero is a number that when subbed in for the x variable it makes the equation equal to zero A zero is another name for an x-intercept

29 Investigate the Math p.373

30 Example 1

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32 Example 2

33 Is it possible for a Quad Equation to have more than 2 roots?

34 Example 3

35 Summary p.379

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37 Practice Ex. 6.3 (p.379) #1-13 #5-15

38 4. Quadratics in Factored Form FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q, including: vertex intercepts domain and range axis of symmetry.

39 Investigate the Math p.382

40 To find your x-intercepts for your quadratic you can factor the function then set each part equal to zero and solve for x. You can then also average your x-intercepts together to get your axis of symmetry

41 Example 1

42 Example 2

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44 Example 3

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46 Example 4

47 Summary p.390

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50 Practice Ex. 7.4 (p.391) #1-16 #4-20

51 5. Solving Quadratics by Factoring FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q, including: vertex intercepts domain and range axis of symmetry.

52 5. Solving Quadratics by Factoring

53 When you rewrite your Quadratic equation in Standard form (=0) you can factor the equation to easily find your zeros (x- intercepts)

54 How can you verify that your answers are correct? If I gave you the roots (x-intercepts) 2 and 6 can you give me the quadratic equation in standard form? Can all quadratic equations be solved by factoring?

55 Example 1

56 Example 2

57 When your quadratic function is in factored from how can you tell how many roots there will be 2 or 1?

58 Example 3

59 Example 4

60 Summary p.405

61 Practice Ex. 7.5 (p.405) #1-15 #3-18

62 6. Vertex Form FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q, including: vertex intercepts domain and range axis of symmetry.

63 6. Vertex Form

64 Investigate the Math p.408 Read problem then go straight to the questions

65 Example 1

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67 Example 2

68 Example 3

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70 Example 4

71 Summary p.416

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74 Practice Ex. 7.6 (p.417) #1-14 #4-19

75 7. The Quadratic Formula FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q, including: vertex intercepts domain and range axis of symmetry.

76 7. The Quadratic Formula When we want to solve a quadratic function, find the roots, zeros or x-intercepts but we can not factor the function we use the Quadratic Formula The Quadratic Formula solve for x when we can not factor

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78 Example 1

79 Example 2

80 Example 3

81 Example 4

82 Summary p.427

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84 Practice Ex. 7.7 (p.427) #1-11 #4-13

85 8. Solving Problems FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)² + q, including: vertex intercepts domain and range axis of symmetry.

86 8. Solving Problems

87 Example 2

88 Example 3

89 Example 4

90 Summary p.436

91 Practice Ex. 7.8 (p.436) #1-8 #2-12


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