1. 9.1 – Graphing Quadratic Functions

2. Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5

3. Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy

4. Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy -2 0 1 2

5. Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy -2 0 1 2

6. Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 y = 2(-2) 2 – 4(-2) – 5 xy -2 0 1 2

7. Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 y = 2(-2) 2 – 4(-2) – 5 y = 8 + 8 – 5 = 11 xy -2 0 1 2

8. Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 y = 2(-2) 2 – 4(-2) – 5 y = 8 + 8 – 5 = 11 xy -211 0 1 2

9. Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 y = 2(-2) 2 – 4(-2) – 5 y = 8 + 8 – 5 = 11 xy -211 1 0-5 1-7 2-5

10. Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy -211 1 0-5 1-7 2-5

11. Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy -211 1 0-5 1-7 2-5

12. Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy -211 1 0-5 1-7 2-5

13. b. y = -x 2 + 4x – 1 xy -2 0 1 2

14. b. y = -x 2 + 4x – 1 xy -2-13 -6 0 12 23

15. b. y = -x 2 + 4x – 1 xy -2-13 -6 0 12 23

16. b. y = -x 2 + 4x – 1 xy -2-13 -6 0 12 23 3 4

17. b. y = -x 2 + 4x – 1 xy -2-13 -6 0 12 23 32 4

18. b. y = -x 2 + 4x – 1 xy -2-13 -6 0 12 23 32 4

19. b. y = -x 2 + 4x – 1 xy -2-13 -6 0 12 23 32 4

20. Axis of symmetry:

21. Axis of symmetry: x = - b 2a

22. Vertex:

23. Axis of symmetry: x = - b 2a Vertex: (x, y)

24. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x = axis of sym.

25. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x = axis of sym. Maximum vs. Minimum:

26. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x = axis of sym. Maximum vs. Minimum: For ax 2 + bx + c,

27. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x = axis of sym. Maximum vs. Minimum: For ax 2 + bx + c, –If a is positive, then the vertex is a Minimum.

28. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x = axis of sym. Maximum vs. Minimum: For ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum.

29. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function.

30. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x 2 + 2x + 3

31. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x 2 + 2x + 3 1) axis of sym.:

32. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x 2 + 2x + 3 1) axis of sym.: x = - b 2a

33. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2 2a 2(-1)

34. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2

35. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex:

36. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y)

37. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1,

38. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?)

39. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x 2 + 2x + 3

40. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x 2 + 2x + 3 -(1) 2 + 2(1) + 3

41. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x 2 + 2x + 3 -(1) 2 + 2(1) + 3 -1 + 2 + 3

42. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x 2 + 2x + 3 -(1) 2 + 2(1) + 3 -1 + 2 + 3 = 4

43. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x 2 + 2x + 3 -(1) 2 + 2(1) + 3 -1 + 2 + 3 = 4, so (1, 4)

44. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x 2 + 2x + 3 -(1) 2 + 2(1) + 3 -1 + 2 + 3 = 4, so (1, 4) 3) Max OR Min.?

45. Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x 2 + 2x + 3 -(1) 2 + 2(1) + 3 -1 + 2 + 3 = 4, so (1, 4) 3) Max OR Min.? (1, 4) is a max b/c a is neg.

46. 4) Graph:

47. *Plot vertex:

48. 4) Graph: *Plot vertex: (1, 4)

49. 4) Graph: *Plot vertex: (1, 4) *Make a table based on vertex

50. 4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 14

51. 4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 0 14

52. 4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 0 14

53. 4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 0 14 2

54. 4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 0 14 2 3

55. 4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 0 03 14 23 30

56. 4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 0 03 14 23 30

57. 4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 0 03 14 23 30

58. b. 2x 2 – 4x – 5

59. 1) axis of sym.: 2) vertex: (x, y) = 3) Max OR Min.? 4) Graph:

60. b. 2x 2 – 4x – 5 1) axis of sym.: x = - b = -(-4)= 4 = 1 2a 2(2) 4 2) vertex: (x, y) = (1, ?) 2x 2 – 4x – 5 2(1) 2 – 4(1) – 5 2 – 4 – 5 = -7, so (1, -7) 3) Max OR Min.? (1, -7) is a min b/c a is neg. 4) Graph: *Plot vertex: (1, -7) * Make a table based on vertex xy 1 0-5 1-7 2-5 31