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9.1 – Graphing Quadratic Functions

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

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9.1 – Graphing Quadratic Functions

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  1. 9.1 – Graphing Quadratic Functions

  2. Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5

  3. Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5

  4. Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5

  5. Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5

  6. Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5 y = 2(-2)2 – 4(-2) – 5

  7. Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5 y = 2(-2)2 – 4(-2) – 5 y = 8 + 8 – 5 = 11

  8. Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5 y = 2(-2)2 – 4(-2) – 5 y = 8 + 8 – 5 = 11

  9. Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5 y = 2(-2)2 – 4(-2) – 5 y = 8 + 8 – 5 = 11

  10. Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5

  11. Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5

  12. Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5

  13. b. y = -x2 + 4x – 1

  14. b. y = -x2 + 4x – 1

  15. b. y = -x2 + 4x – 1

  16. b. y = -x2 + 4x – 1

  17. b. y = -x2 + 4x – 1

  18. b. y = -x2 + 4x – 1

  19. b. y = -x2 + 4x – 1

  20. Axis of symmetry:

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

  22. Axis of symmetry: x = - b 2a • 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 ax2 + bx + c,

  27. Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x = axis of sym. • Maximum vs. Minimum: For ax2 + 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 ax2 + 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 ax2 + 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 ax2 + 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. -x2 + 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 ax2 + 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. -x2 + 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 ax2 + 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. -x2 + 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 ax2 + 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. -x2 + 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 ax2 + 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. -x2 + 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 ax2 + 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. -x2 + 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 ax2 + 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. -x2 + 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 ax2 + 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. -x2 + 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 ax2 + 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. -x2 + 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 ax2 + 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. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x2 + 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 ax2 + 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. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x2 + 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 ax2 + 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. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x2 + 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 ax2 + 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. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x2 + 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 ax2 + 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. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x2 + 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 ax2 + 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. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x2 + 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 ax2 + 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. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x2 + 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. 4) Graph: *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

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