1. F. Everything Quadratics
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.

2. Getting Started
String Art p.356

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?
Quadratic Relation – A relation that can be written in the standard form𝑦=𝑎 𝑥 2 +𝑏𝑥+𝑐, where 𝑎≠0; for example, 𝑦=4 𝑥 2 +2𝑥+1
Parabola – The shape of the graph of any quadratic relation.

9. Explore the Math p.359
Grab your graphing Calculators!!
How does changing the coefficients and constant in a relation that is written in the form 𝑦=𝑎 𝑥 2 +𝑏𝑥+𝑐affect the graph of the relation?

10. Summary p.359

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.

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?

21. Example 3

23. Summary p.368

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

32. Example 2

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

34. Example 3

35. Summary p.379

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

44. Example 3

46. Example 4

47. Summary p.390

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
Vertex Form of a Quadratic Function
𝑦=𝑎 (𝑥−ℎ) 2 +𝑘

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

65. Example 1

67. Example 2

68. Example 3

70. Example 4

71. Summary p.416

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

77. Quadratic Formula:
𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎
When 𝑎 𝑥 2 +𝑏𝑥+𝑐=0

78. Example 1

79. Example 2

80. Example 3

81. Example 4

82. Summary p.427

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