11 x1 t10 01 graphing quadratics (2012)

Download 11 x1 t10 01 graphing quadratics (2012)

Post on 04-Jul-2015

544 views

Category:

Education

2 download

Embed Size (px)

TRANSCRIPT

  • 1. The Quadratic Polynomialand the Parabola

2. The Quadratic Polynomial and the ParabolaQuadratic polynomial 3. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx c 4. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx cQuadratic function 5. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx cQuadratic function y ax 2 bx c 6. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx cQuadratic function y ax 2 bx cQuadratic equation 7. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx cQuadratic function y ax 2 bx cQuadratic equation ax 2 bx c 0 8. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx cQuadratic function y ax 2 bx cQuadratic equation ax 2 bx c 0Coefficients 9. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx cQuadratic function y ax 2 bx cQuadratic equation ax 2 bx c 0Coefficients a, b, c 10. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx cQuadratic function y ax 2 bx cQuadratic equation ax 2 bx c 0Coefficients a, b, cIndeterminate 11. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx cQuadratic function y ax 2 bx cQuadratic equation ax 2 bx c 0Coefficients a, b, cIndeterminate x 12. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx cQuadratic function y ax 2 bx cQuadratic equation ax 2 bx c 0Coefficients a, b, cIndeterminate xRoots 13. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx cQuadratic function y ax 2 bx cQuadratic equation ax 2 bx c 0Coefficients a, b, cIndeterminate xRoots Solutions to the quadratic equation 14. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx cQuadratic function y ax 2 bx cQuadratic equation ax 2 bx c 0Coefficients a, b, cIndeterminate xRoots Solutions to the quadratic equation Zeroes 15. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx cQuadratic function y ax 2 bx cQuadratic equation ax 2 bx c 0Coefficients a, b, cIndeterminate xRoots Solutions to the quadratic equation Zeroes x intercepts of the quadratic function 16. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx cQuadratic function y ax 2 bx cQuadratic equation ax 2 bx c 0Coefficients a, b, cIndeterminate xRoots Solutions to the quadratic equation Zeroes x intercepts of the quadratic function e.g. Find the roots of x 2 1 0 17. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx cQuadratic function y ax 2 bx cQuadratic equation ax 2 bx c 0Coefficients a, b, cIndeterminate xRoots Solutions to the quadratic equation Zeroes x intercepts of the quadratic function e.g. Find the roots of x 2 1 0x2 1 0x2 1 18. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx cQuadratic function y ax 2 bx cQuadratic equation ax 2 bx c 0Coefficients a, b, cIndeterminate xRoots Solutions to the quadratic equation Zeroes x intercepts of the quadratic function e.g. Find the roots of x 2 1 0x2 1 0x2 1 x 1 19. The Quadratic Polynomial and the ParabolaQuadratic polynomial ax 2 bx cQuadratic function y ax 2 bx cQuadratic equation ax 2 bx c 0Coefficients a, b, cIndeterminate xRoots Solutions to the quadratic equation Zeroes x intercepts of the quadratic function e.g. Find the roots of x 2 1 0x2 1 0x2 1 x 1 the roots are x 1 and x 1 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. y ax 2 bx c 23. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx ca 24. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx cya x 25. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx cya xa0 26. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx cyaxa0concave up 27. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx cyyaxxa0concave up 28. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx cyyaxxa0a0concave up 29. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx cyyaxxa0 a0concave up concave down 30. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx cyyaxxa0 a0concave up concave downc 31. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx cyyaxxa0 a0concave up concave downc = y intercept 32. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx cyyaxxa0 a0concave up concave downc = y interceptzeroes (roots) 33. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx cyyaxxa0 a0concave up concave downc = y interceptzeroes (roots) = x intercepts 34. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx cyyaxxa0 a0concave up concave downc = y interceptzeroes (roots) = x intercepts bx 2a 35. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx cyyaxxa0 a0concave up concave downc = y interceptzeroes (roots) = x intercepts bx= axis of symmetry 2a 36. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx cyyaxxa0a0concave upconcave downc = y interceptzeroes (roots) = x intercepts bx= axis of symmetry Note: AOS is the average of the zeroes 2a 37. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx cyyaxxa0a0concave upconcave downc = y interceptzeroes (roots) = x intercepts bx= axis of symmetry Note: AOS is the average of the zeroes 2a vertex 38. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx cyyaxxa0a0concave upconcave downc = y interceptzeroes (roots) = x intercepts bx= axis of symmetry Note: AOS is the average of the zeroes 2a vertex x value is the AOS 39. Graphing QuadraticsThe graph of a quadratic function is a parabola. y ax 2 bx cyyax xa0a0concave upconcave downc = y interceptzeroes (roots) = x intercepts bx= axis of symmetry Note: AOS is the average of the zeroes 2a vertex 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. y ax 2 bx cyyax xa0a0concave upconcave downc = y interceptzeroes (roots) = x intercepts bx= axis of symmetry Note: AOS is the average of the zeroes 2a vertex 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. Graph y x 2 8 x 12 42. e.g. Graph y x 2 8 x 12a=1>0yx 43. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upyx 44. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upc = 12 y y x 2 8 x 12 x 45. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upc = 12 y intercept is 0,12 yx 46. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upc = 12 y intercept is 0,12 y 12x 47. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upc = 12 y intercept is 0,12 zeroesy 12x 48. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upc = 12 y intercept is 0,12 zeroes x 2 8 x 12 0 y y x 2 8 x 12 12x 49. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upc = 12 y intercept is 0,12 zeroes x 2 8 x 12 0 y y x 2 8 x 12 x 6 x 2 012x 50. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upc = 12 y intercept is 0,12 zeroes x 2 8 x 12 0 y y x 2 8 x 12 x 6 x 2 012x 6 or x 2x 51. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upc = 12 y intercept is 0,12 zeroes x 2 8 x 12 0 y y x 2 8 x 12 x 6 x 2 012x 6 or x 2 x intercepts are 6,0 and 2,0 x 52. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upc = 12 y intercept is 0,12 zeroes x 2 8 x 12 0 y y x 2 8 x 12 x 6 x 2 012x 6 or x 2 x intercepts are 6,0 and 2,0 6 2 x 53. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upc = 12 y intercept is 0,12 zeroes x 2 8 x 12 0 y y x 2 8 x 12 x 6 x 2 012x 6 or x 2 x intercepts are 6,0 and 2,0 AOS6 2 x 54. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upc = 12 y intercept is 0,12 zeroes x 2 8 x 12 0 y y x 2 8 x 12 x 6 x 2 012x 6 or x 2 x intercepts are 6,0 and 2,0 AOS x b2a6 2 x 55. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upc = 12 y intercept is 0,12 zeroes x 2 8 x 12 0 y y x 2 8 x 12 x 6 x 2 012x 6 or x 2 x intercepts are 6,0 and 2,0 AOS x b2a8 26 2 x 4 56. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upc = 12 y intercept is 0,12 zeroes x 2 8 x 12 0 y y x 2 8 x 12 x 6 x 2 012x 6 or x 2 x intercepts are 6,0 and 2,0 AOS x bOR x 6 22a 28 26 2 x 4 57. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upc = 12 y intercept is 0,12 zeroes x 2 8 x 12 0 y y x 2 8 x 12 x 6 x 2 012x 6 or x 2 x intercepts are 6,0 and 2,0 AOS x bOR x 6 22a 28 4 26 2 x 4 58. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upc = 12 y intercept is 0,12 zeroes x 2 8 x 12 0 y y x 2 8 x 12 x 6 x 2 012x 6 or x 2 x intercepts are 6,0 and 2,0 AOS x bOR x 6 22a 28 4 26 2 x 4 59. e.g. Graph y x 2 8 x 12a = 1 > 0 concave upc = 12 y intercept is 0,12 zeroes x 2 8 x 12 0 y y x 2 8 x 12 x 6 x 2 012x 6 or x 2 x intercepts are 6,0 and 2,0 AOS x bOR x 6 22a 28 4 26 2 x 4vertex 60. e.g. Graph y x 2 8 x 12a = 1 > 0 concave up c = 12 y intercept is 0,12 zeroes x 2 8 x 12 0y y x 2 8 x 12 x 6 x 2 0 12x 6 or x 2 x intercepts are 6,0 and 2,0 AOS x bOR x 6 22a 28 4 2 6 2 x 4y 4 8 4 12 2vertex 61. e.g. Graph y x 2 8 x 12a = 1 > 0 concave up c = 12 y intercept is 0,12 zeroes x 2 8 x 12 0y y x 2 8 x 12 x 6 x 2 0 12x 6 or x 2 x intercepts are 6,0 and 2,0 AOS x b OR x 6 22a28 4 2 6 2 x 4y 4 8 4 12 2vertex 4 62. e.g. Graph y x 2 8 x 12a = 1 > 0 concave up c = 12 y intercept is 0,12 zeroes x 2 8 x 12 0y y x 2 8 x 12 x 6 x 2 0 12x 6 or x 2 x intercepts are 6,0 and 2,0 AOS x bOR x 6 22a 28 4 2 6 2 x 4y 4 8 4 12 2vertex 4 vertex is 4, 4 63. e.g. Graph y x 2 8 x 12a = 1 > 0 concave up c = 12 y intercept is 0,12 zeroes x 2 8 x 12 0 y y x 2 8 x 12 x 6 x 2 0 12x 6 or x 2 x intercepts are 6,0 and 2,0 AOS x bOR x 6 22a 28 4 2 62 x 4y 4 8 4 12 2vertex(4, 4) 4 vertex is 4, 4 64. e.g. Graph y x 2 8 x 12a = 1 > 0 concave up c = 12 y intercept is 0,12 zeroes x 2 8 x 12 0 y y x 2 8 x 12 x 6 x 2 0 12x 6 or x 2 x intercepts are 6,0 and 2,0 AOS x bOR x 6 22a 28 4 2 62 x 4y 4 8 4 12 2vertex(4, 4) 4 vertex is 4, 4 65. (ii) Find the quadratic with; a) roots 3 and 6 66. (ii) Find the quadratic with; a) roots 3 and 6 y a x 2 9 x 18 67. (ii) Find the quadratic with; a) roots 3 and 6 y a x 2 9 x 18 6 363 68. (ii) Find the quadratic with; a) roots 3 and 6b) monic roots 3 2 and 3 2 y a x 2 9 x 18 6 363 69. (ii) Find the quadratic with;a) roots 3 and 6b) monic roots 3 2 and 3 2y a x 2 9 x 18 y x2 6x 7 6 363c) roots 2 and 8 and vertex (5,3) y a x 2 10 x 16 5,3 : 3 a 52 10 5 16 3 9a 1a 3 y x 10 x 16 1 2 3 70. (ii) Find the quadratic with; a) roots 3 and 6b) monic roots 3 2 and 3 2 y a x 2 9 x 18 y x2 6x 7 6 363 3 2 3 2 3 2 3 2 71. (ii) Find the quadratic with; a) roots 3 and 6b) monic roots 3 2 and 3 2 y a x 2 9 x 18 y x2 6x 7 6 363 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 6b) monic roots 3 2 and 3 2 y a x 2 9 x 18 y x2 6x 7 6 363 3 2 3 2 3 2 3 2 c) roots 2 and 8 and vertex (5,3)y a x 2 10 x 16 73. (ii) Find the quadratic with;a) roots 3 and 6b) monic roots 3 2 and 3 2y a x 2 9 x 18 y x2 6x 7 6 363 3 2 3 2 3 2 3 2 c) roots 2 and 8 and vertex (5,3) y a x 2 10 x 16 5,3 : 3 a 52 10 5 16 74. (ii) Find the quadratic with;a) roots 3 and 6b) monic roots 3 2 and 3 2y a x 2 9 x 18 y x2 6x 7 6 363 3 2 3 2 3 2 3 2 c) roots 2 and 8 and vertex (5,3) y a x 2 10 x 16 5,3 : 3 a 52 10 5 16 3 9a 1a 3 75. (ii) Find the quadratic with;a) roots 3 and 6b) monic roots 3 2 and 3 2y a x 2 9 x 18 y x2 6x 7 6 363 3 2 3 2 3 2 3 2 c) roots 2 and 8 and vertex (5,3) y a x 2 10 x 16 5,3 : 3 a 52 10 5 16 3 9a 1a 3 y x 10 x 16 1 2 3 76. (iii) Solve;a) x 2 5 x 6 0 77. (iii) Solve;a) x 2 5 x 6 0 x 2 x 3 0 78. (iii) Solve;a) x 2 5 x 6 0y x 2 x 3 03 2 x 79. (iii) Solve;a) x 2 5 x 6 0y x 2 x 3 03 2 x 80. (iii) Solve;a) x 2 5 x 6 0 y x 2 x 3 0 3 2xQ: for what values of x is the parabola above the x axis? 81. (iii) Solve;a) x 2 5 x 6 0 y x 2 x 3 0 3 2xQ: for what values of x is the parabola above the x axis? 82. (iii) Solve;a) x 2 5 x 6 0 y x 2 x 3 0 x 3 or x 23 2xQ: for what values of x is the parabola above the x axis? 83. (iii) Solve;a) x 2 5 x 6 0 y x 2 x 3 0 x 3 or x 23 2xQ: for what values of x is the parabola above the x axis? b) x 2 3 x 4 84. (iii) Solve;a) x 2 5 x 6 0 y x 2 x 3 0 x 3 or x 23 2xQ: for what values of x is the parabola above the x axis? b) x 2 3 x 4 x 2 3x 4 0 85. (iii) Solve;a) x 2 5 x 6 0 y x 2 x 3 0 x 3 or x 23 2xQ: for what values of x is the parabola above the x axis? b) x 2 3 x 4x 2 3x 4 0 x 4 x 1 0 86. (iii) Solve;a) x 2 5 x 6 0 y x 2 x 3 0 x 3 or x 23 2xQ: for what values of x is the parabola above the x axis? b) x 2 3 x 4 yx 2 3x 4 0 x 4 x 1 0 41x 87. (iii) Solve;a) x 2 5 x 6 0 y x 2 x 3 0 x 3 or x 23 2xQ: for what values of x is the parabola above the x axis? b) x 2 3 x 4 yx 2 3x 4 0 x 4 x 1 0 41x 88. (iii) Solve;a) x 2 5 x 6 0y x 2 x 3 0 x 3 or x 23 2xQ: for what values of x is the parabola above the x axis? b) x 2 3 x 4yx 2 3x 4 0 x 4 x 1 041xQ: for what values of x is the parabola below the x axis? 89. (iii) Solve;a) x 2 5 x 6 0y x 2 x 3 0 x 3 or x 23 2xQ: for what values of x is the parabola above the x axis? b) x 2 3 x 4yx 2 3x 4 0 x 4 x 1 041xQ: for what values of x is the parabola below the x axis? 90. (iii) Solve;a) x 2 5 x 6 0y x 2 x 3 0 x 3 or x 23 2xQ: for what values of x is the parabola above the x axis? b) x 2 3 x 4yx 2 3x 4 0 x 4 x 1 0 4 x 1 41xQ: for what values of x is the parabola below the x axis? 91. Exercise 8A; 1adf, 2adf, 3bd, 4bd, 5c, 6ade, 7d, 9ace, 12c,13b, 14a

Recommended

View more >