11 x1 t10 01 graphing quadratics (2013)

  • 405 views
Uploaded on

 

More in: Education , Technology
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Be the first to comment
    Be the first to like this
No Downloads

Views

Total Views
405
On Slideshare
0
From Embeds
0
Number of Embeds
1

Actions

Shares
Downloads
7
Comments
0
Likes
0

Embeds 0

No embeds

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
    No notes for slide

Transcript

  • 1. The Quadratic Polynomialand the Parabola
  • 2. The Quadratic Polynomialand the ParabolaQuadratic polynomial –
  • 3. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c 
  • 4. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c Quadratic function –
  • 5. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c Quadratic function – 2y ax bx c  
  • 6. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c Quadratic function – 2y ax bx c  Quadratic equation –
  • 7. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c Quadratic function – 2y ax bx c  Quadratic equation – 20ax bx c  
  • 8. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c Quadratic function – 2y ax bx c  Quadratic equation – 20ax bx c  Coefficients –
  • 9. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c Quadratic function – 2y ax bx c  Quadratic equation – 20ax bx c  , ,a b cCoefficients –
  • 10. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c Quadratic function – 2y ax bx c  Quadratic equation – 20ax bx c  , ,a b cCoefficients –Indeterminate –
  • 11. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c Quadratic function – 2y ax bx c  Quadratic equation – 20ax bx c  , ,a b cCoefficients –xIndeterminate –
  • 12. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c Quadratic function – 2y ax bx c  Quadratic equation – 20ax bx c  , ,a b cCoefficients –xIndeterminate –Roots –
  • 13. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c Quadratic function – 2y ax bx c  Quadratic equation – 20ax bx c  , ,a b cCoefficients –xIndeterminate –Roots – Solutions to the quadratic equation
  • 14. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c Quadratic function – 2y ax bx c  Quadratic equation – 20ax bx c  , ,a b cCoefficients –xIndeterminate –Roots – Solutions to the quadratic equationZeroes –
  • 15. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c Quadratic function – 2y ax bx c  Quadratic equation – 20ax bx c  , ,a b cCoefficients –xIndeterminate –Roots – Solutions to the quadratic equationZeroes – x intercepts of the quadratic function
  • 16. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c Quadratic function – 2y ax bx c  Quadratic equation – 20ax bx c  , ,a b cCoefficients –xIndeterminate –Roots – Solutions to the quadratic equationZeroes – x intercepts of the quadratic function2e.g. Find the roots of 1 0x  
  • 17. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c Quadratic function – 2y ax bx c  Quadratic equation – 20ax bx c  , ,a b cCoefficients –xIndeterminate –Roots – Solutions to the quadratic equationZeroes – x intercepts of the quadratic function2e.g. Find the roots of 1 0x  221 01xx 
  • 18. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c Quadratic function – 2y ax bx c  Quadratic equation – 20ax bx c  , ,a b cCoefficients –xIndeterminate –Roots – Solutions to the quadratic equationZeroes – x intercepts of the quadratic function2e.g. Find the roots of 1 0x  221 01xx 1x  
  • 19. The Quadratic Polynomialand the ParabolaQuadratic polynomial – 2ax bx c Quadratic function – 2y ax bx c  Quadratic equation – 20ax bx c  , ,a b cCoefficients –xIndeterminate –Roots – Solutions to the quadratic equationZeroes – x intercepts of the quadratic function2e.g. Find the roots of 1 0x  221 01xx 1x   the roots are 1 and 1x x   
  • 20. Graphing Quadratics
  • 21. Graphing QuadraticsThe graph of a quadratic function is a parabola.
  • 22. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  
  • 23. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  a
  • 24. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx
  • 25. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx0a 
  • 26. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx0a concave up
  • 27. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx0a concave upyx
  • 28. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx0a concave up0a yx
  • 29. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx0a concave up0a yxconcave down
  • 30. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx0a concave up0a yxconcave downc
  • 31. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx0a concave up0a yxconcave downc = y intercept
  • 32. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx0a concave up0a yxconcave downc = y interceptzeroes (roots)
  • 33. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx0a concave up0a yxconcave downc = y interceptzeroes (roots) = x intercepts
  • 34. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx0a concave up0a yxconcave downc = y interceptzeroes (roots) = x intercepts2bxa
  • 35. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx0a concave up0a yxconcave downc = y interceptzeroes (roots) = x intercepts2bxa = axis of symmetry
  • 36. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx0a concave up0a yxconcave downc = y interceptzeroes (roots) = x intercepts2bxa = axis of symmetry Note: AOS is the average of the zeroes
  • 37. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx0a concave up0a yxconcave downc = y interceptzeroes (roots) = x intercepts2bxa = axis of symmetry Note: AOS is the average of the zeroesvertex
  • 38. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx0a concave up0a yxconcave downc = y interceptzeroes (roots) = x intercepts2bxa = axis of symmetry Note: AOS is the average of the zeroesvertex x value is the AOS
  • 39. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx0a concave up0a yxconcave downc = y interceptzeroes (roots) = x intercepts2bxa = axis of symmetry Note: AOS is the average of the zeroesvertex x value is the AOSy value is found by substituting AOS into the function.
  • 40. Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c  ayx0a concave up0a yxconcave downc = y interceptzeroes (roots) = x intercepts2bxa = axis of symmetry Note: AOS is the average of the zeroesvertex x value is the AOSy value is found by substituting AOS into the function.(It is the maximum/minimum value of the function)
  • 41. e.g. 2Graph 8 12y x x  
  • 42. e.g. 2Graph 8 12y x x  a = 1 > 0yx
  • 43. e.g. 2Graph 8 12y x x  a = 1 > 0 concave upyx
  • 44. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12yx28 12y x x  
  • 45. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yyx
  • 46. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yyx12
  • 47. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes yx12
  • 48. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x   yx1228 12y x x  
  • 49. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x    6 2 0x x  yx1228 12y x x  
  • 50. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x    6 2 0x x  6 or 2x x   yx1228 12y x x  
  • 51. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x    6 2 0x x  6 or 2x x      intercepts are6,0 and 2,0x yx1228 12y x x  
  • 52. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x    6 2 0x x  6 or 2x x      intercepts are6,0 and 2,0x yx12–2–628 12y x x  
  • 53. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x    6 2 0x x  6 or 2x x      intercepts are6,0 and 2,0x AOSyx12–2–628 12y x x  
  • 54. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x    6 2 0x x  6 or 2x x      intercepts are6,0 and 2,0x AOS2bxayx12–2–628 12y x x  
  • 55. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x    6 2 0x x  6 or 2x x      intercepts are6,0 and 2,0x AOS2bxa824 yx12–2–628 12y x x  
  • 56. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x    6 2 0x x  6 or 2x x      intercepts are6,0 and 2,0x AOS2bxa824 OR6 22x yx12–2–628 12y x x  
  • 57. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x    6 2 0x x  6 or 2x x      intercepts are6,0 and 2,0x AOS2bxa824 OR6 22x 4 yx12–2–628 12y x x  
  • 58. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x    6 2 0x x  6 or 2x x      intercepts are6,0 and 2,0x AOS2bxa824 OR6 22x 4 yx12–2–628 12y x x  
  • 59. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x    6 2 0x x  6 or 2x x      intercepts are6,0 and 2,0x AOS2bxa824 OR6 22x 4 vertexyx12–2–628 12y x x  
  • 60. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x    6 2 0x x  6 or 2x x      intercepts are6,0 and 2,0x AOS2bxa824 OR6 22x 4 vertex    24 8 4 12y     yx12–2–628 12y x x  
  • 61. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x    6 2 0x x  6 or 2x x      intercepts are6,0 and 2,0x AOS2bxa824 OR6 22x 4 vertex    24 8 4 12y     4 yx12–2–628 12y x x  
  • 62. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x    6 2 0x x  6 or 2x x      intercepts are6,0 and 2,0x AOS2bxa824 OR6 22x 4 vertex    24 8 4 12y     4  vertex is 4, 4  yx12–2–628 12y x x  
  • 63. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x    6 2 0x x  6 or 2x x      intercepts are6,0 and 2,0x AOS2bxa824 OR6 22x 4 vertex    24 8 4 12y     4  vertex is 4, 4  yx12–2–6(–4, –4)28 12y x x  
  • 64. e.g. 2Graph 8 12y x x  a = 1 > 0 concave up c = 12  intercept is 0,12yzeroes 28 12 0x x    6 2 0x x  6 or 2x x      intercepts are6,0 and 2,0x AOS2bxa824 OR6 22x 4 vertex    24 8 4 12y     4  vertex is 4, 4  yx12–2–6(–4, –4)28 12y x x  
  • 65. (ii) Find the quadratic with;a) roots 3 and 6
  • 66. (ii) Find the quadratic with;a) roots 3 and 6 29 18y a x x  
  • 67. (ii) Find the quadratic with;a) roots 3 and 6 29 18y a x x   6 3  6 3
  • 68. (ii) Find the quadratic with;a) roots 3 and 6 29 18y a x x   6 3  6 3b) monic roots 3 2 and 3 2 
  • 69. (ii) Find the quadratic with;a) roots 3 and 6 29 18y a x x   6 3  6 3b) monic roots 3 2 and 3 2 26 7y x x  c) roots 2 and 8 and vertex (5,3) 210 16y a x x      25,3 : 3 5 10 5 16a  3 913aa   2110 163y x x    
  • 70. (ii) Find the quadratic with;a) roots 3 and 6 29 18y a x x   6 3  6 3b) monic roots 3 2 and 3 2 26 7y x x   3 2 3 2     3 2 3 2 
  • 71. (ii) Find the quadratic with;a) roots 3 and 6 29 18y a x x   6 3  6 3b) monic roots 3 2 and 3 2 26 7y x x   3 2 3 2     3 2 3 2 c) roots 2 and 8 and vertex (5,3)
  • 72. (ii) Find the quadratic with;a) roots 3 and 6 29 18y a x x   6 3  6 3b) monic roots 3 2 and 3 2 26 7y x x   3 2 3 2     3 2 3 2 c) roots 2 and 8 and vertex (5,3) 210 16y a x x  
  • 73. (ii) Find the quadratic with;a) roots 3 and 6 29 18y a x x   6 3  6 3b) monic roots 3 2 and 3 2 26 7y x x   3 2 3 2     3 2 3 2 c) roots 2 and 8 and vertex (5,3) 210 16y a x x      25,3 : 3 5 10 5 16a  
  • 74. (ii) Find the quadratic with;a) roots 3 and 6 29 18y a x x   6 3  6 3b) monic roots 3 2 and 3 2 26 7y x x   3 2 3 2     3 2 3 2 c) roots 2 and 8 and vertex (5,3) 210 16y a x x      25,3 : 3 5 10 5 16a  3 913aa  
  • 75. (ii) Find the quadratic with;a) roots 3 and 6 29 18y a x x   6 3  6 3b) monic roots 3 2 and 3 2 26 7y x x   3 2 3 2     3 2 3 2 c) roots 2 and 8 and vertex (5,3) 210 16y a x x      25,3 : 3 5 10 5 16a  3 913aa   2110 163y x x    
  • 76. (iii) Solve;2) 5 6 0a x x  
  • 77. (iii) Solve;2) 5 6 0a x x    2 3 0x x  
  • 78. (iii) Solve;2) 5 6 0a x x    2 3 0x x  yx–3 –2
  • 79. (iii) Solve;2) 5 6 0a x x    2 3 0x x  yx–3 –2
  • 80. (iii) Solve;2) 5 6 0a x x    2 3 0x x  yx–3 –2Q: for what values of x is theparabola above the x axis?
  • 81. (iii) Solve;2) 5 6 0a x x    2 3 0x x  yx–3 –2Q: for what values of x is theparabola above the x axis?
  • 82. (iii) Solve;2) 5 6 0a x x    2 3 0x x  yx–3 –2Q: for what values of x is theparabola above the x axis?3 or 2x x   
  • 83. (iii) Solve;2) 5 6 0a x x    2 3 0x x  yx–3 –2Q: for what values of x is theparabola above the x axis?3 or 2x x   2) 3 4b x x   
  • 84. (iii) Solve;2) 5 6 0a x x    2 3 0x x  yx–3 –2Q: for what values of x is theparabola above the x axis?3 or 2x x   2) 3 4b x x   23 4 0x x  
  • 85. (iii) Solve;2) 5 6 0a x x    2 3 0x x  yx–3 –2Q: for what values of x is theparabola above the x axis?3 or 2x x   2) 3 4b x x     4 1 0x x  23 4 0x x  
  • 86. (iii) Solve;2) 5 6 0a x x    2 3 0x x  yx–3 –2Q: for what values of x is theparabola above the x axis?3 or 2x x   2) 3 4b x x     4 1 0x x  yx1–423 4 0x x  
  • 87. (iii) Solve;2) 5 6 0a x x    2 3 0x x  yx–3 –2Q: for what values of x is theparabola above the x axis?3 or 2x x   2) 3 4b x x     4 1 0x x  yx1–423 4 0x x  
  • 88. (iii) Solve;2) 5 6 0a x x    2 3 0x x  yx–3 –2Q: for what values of x is theparabola above the x axis?3 or 2x x   2) 3 4b x x     4 1 0x x  yx1–4Q: for what values of x is theparabola below the x axis?23 4 0x x  
  • 89. (iii) Solve;2) 5 6 0a x x    2 3 0x x  yx–3 –2Q: for what values of x is theparabola above the x axis?3 or 2x x   2) 3 4b x x     4 1 0x x  yx1–4Q: for what values of x is theparabola below the x axis?23 4 0x x  
  • 90. (iii) Solve;2) 5 6 0a x x    2 3 0x x  yx–3 –2Q: for what values of x is theparabola above the x axis?3 or 2x x   2) 3 4b x x     4 1 0x x  yx1–4Q: for what values of x is theparabola below the x axis?4 1x  23 4 0x x  
  • 91. Exercise 8A; 1adf, 2adf, 3bd, 4bd, 5c, 6ade, 7d, 9ace, 12c,13b, 14a