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Solving Quadratic Inequalities with Visual Demonstration

Solving Quadratic Inequalities with Visual Demonstration
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2017-01-28 01:22
FunctionCoordinate GeometryInequalityGraphing
This GeoGebra example dynamically demonstrates the solution of quadratic inequalities, visually linking the parabola graph to the inequality solution set. Core mathematical concepts include quadratic functions, one-variable quadratic inequalities, interval notation, and visualization of solution sets on the number line. Construction highlights: commands such as Join, Sort, Element, Simplify, RandomElement, Remove, If, Intersect, and TableText are used to manage data lists, simplify expressions, generate random coefficients, determine intersection points, and produce result tables. Multiple points (e.g., A12-A15, B12-B15) and lists (list1, list7) are involved to build the dynamic figure. Suitable for high school students learning quadratic functions and inequalities, this example helps bridge algebraic solutions with geometric representations, and is ideal for classroom demonstrations or self-directed exploration.

GeoGebra Commands & Parameters

  1. Join({list1, {"None"}}) → list7
  2. Sort(N', Sequence[random(), i, 1, 10]) → N_2
  3. Element(N_2, A15) → B15
  4. Simplify(((x - B15) * (x - C15))) → D15
  5. Element(N_2, A14) → B14
  6. Simplify(((x - B14) * (x - C14))) → D14
  7. Element(N_2, A13) → B13
  8. Simplify(((x - B13) * (x - C13))) → D13
  9. Element(N_2, A12) → B12
  10. Simplify(((x - B12) * (x - C12))) → D12
  11. Join({N', (-N')}) → N
  12. RandomElement(N) → B20
  13. Simplify(((x - B20) * (x - C20))) → D20
  14. RandomElement(N) → B19
  15. Simplify(((x - B19) * (x - C19))) → D19
  16. RandomElement(N) → B10
  17. RandomElement(Remove[N, {(-B10)}]) → C10
  18. Simplify(((-(x - B10)) * (x - C10))) → D10
  19. RandomElement(N) → B9
  20. RandomElement(Remove[N, {(-B9)}]) → C9
  21. Simplify(((-(x - B9)) * (x - C9))) → D9
  22. RandomElement(N) → B5
  23. RandomElement(Remove[N, {B5}]) → C5
  24. Simplify(((x - B5) * (x - C5))) → D5
  25. RandomElement(N) → B18
  26. Simplify(((x - B18) * (x - C18))) → D18
  27. RandomElement(N) → B17
  28. Simplify(((x - B17) * (x - C17))) → D17
  29. RandomElement(N) → B8
  30. RandomElement(Remove[N, {(-B8)}]) → C8
  31. Simplify(((-(x - B8)) * (x - C8))) → D8
  32. RandomElement(N) → B7
  33. RandomElement(Remove[N, {(-B7)}]) → C7
  34. Simplify(((-(x - B7)) * (x - C7))) → D7
  35. RandomElement(N) → B2
  36. RandomElement(Remove[N, {B2}]) → C2
  37. Simplify(((x - B2) * (x - C2))) → D2
  38. RandomElement(N) → B3
  39. RandomElement(Remove[N, {B3}]) → C3
  40. Simplify(((x - B3) * (x - C3))) → D3
  41. RandomElement(N) → B4
  42. RandomElement(Remove[N, {B4}]) → C4
  43. Simplify(((x - B4) * (x - C4))) → D4
  44. RandomElement(T_1) → E2
  45. RandomElement(T_2) → E3
  46. RandomElement(T_1) → E7
  47. RandomElement(T_2) → E8
  48. RandomElement(T_1) → E12
  49. RandomElement(T_2) → E13
  50. RandomElement(T_1) → E17
  51. RandomElement(T_2) → E18
  52. Remove(N, {-5}) → list2
  53. RandomElement(T_1) → E4
  54. RandomElement(T_2) → E5
  55. RandomElement(T_1) → E9
  56. RandomElement(T_2) → E10
  57. RandomElement(T_1) → E14
  58. RandomElement(T_2) → E15
  59. RandomElement(T_1) → E19
  60. RandomElement(T_2) → E20
  61. If(E2 ≟ "lt", H2, If[E2 ≟ "gt", I2, If[E2 ≟ "leqslant", J2, K2]]) → L2
  62. If(E3 ≟ "lt", H3, If[E3 ≟ "gt", I3, If[E3 ≟ "leqslant", J3, K3]]) → L3
  63. If(E4 ≟ "lt", H4, If[E4 ≟ "gt", I4, If[E4 ≟ "leqslant", J4, K4]]) → L4
  64. If(E5 ≟ "lt", H5, If[E5 ≟ "gt", I5, If[E5 ≟ "leqslant", J5, K5]]) → L5
  65. If(E7 ≟ "lt", H7, If[E7 ≟ "gt", I7, If[E7 ≟ "leqslant", J7, K7]]) → L7
  66. If(E8 ≟ "lt", H8, If[E8 ≟ "gt", I8, If[E8 ≟ "leqslant", J8, K8]]) → L8
  67. If(E9 ≟ "lt", H9, If[E9 ≟ "gt", I9, If[E9 ≟ "leqslant", J9, K9]]) → L9
  68. If(E10 ≟ "lt", H10, If[E10 ≟ "gt", I10, If[E10 ≟ "leqslant", J10, K10]]) → L10
  69. If(E12 ≟ "lt", H12, If[E12 ≟ "gt", I12, If[E12 ≟ "leqslant", J12, K12]]) → L12
  70. If(E13 ≟ "lt", H13, If[E13 ≟ "gt", I13, If[E13 ≟ "leqslant", J13, K13]]) → L13
  71. If(E14 ≟ "lt", H14, If[E14 ≟ "gt", I14, If[E14 ≟ "leqslant", J14, K14]]) → L14
  72. If(E15 ≟ "lt", H15, If[E15 ≟ "gt", I15, If[E15 ≟ "leqslant", J15, K15]]) → L15
  73. If(E17 ≟ "lt", H17, If[E17 ≟ "gt", I17, If[E17 ≟ "leqslant", J17, K17]]) → L17
  74. If(E18 ≟ "lt", H18, If[E18 ≟ "gt", I18, If[E18 ≟ "leqslant", J18, K18]]) → L18
  75. If(E19 ≟ "lt", H19, If[E19 ≟ "gt", I19, If[E19 ≟ "leqslant", J19, K19]]) → L19
  76. If(E20 ≟ "lt", H20, If[E20 ≟ "gt", I20, If[E20 ≟ "leqslant", J20, K20]]) → L20
  77. If(a, L2, "?") → E23
  78. If(a, L3, "?") → E24
  79. If(a, L4, "?") → E25
  80. If(a, L5, "?") → E26
  81. If(a, L7, "?") → E28
  82. If(a, L8, "?") → E29
  83. If(a, L9, "?") → E30
  84. If(a, L10, "?") → E31
  85. If(a, L12, "?") → E33
  86. If(a, L13, "?") → E34
  87. If(a, L14, "?") → E35
  88. If(a, L15, "?") → E36
  89. If(a, L17, "?") → E38
  90. If(a, L18, "?") → E39
  91. If(a, L19, "?") → E40
  92. If(a, L20, "?") → E41
  93. Element(list5, SelectedIndex[list7]) → f
  94. Intersect(f, xAxis) → A, B
  95. TableText({list1, list3, If[d, list6, {}], list4}, "cv") → text2

AI Drawing Prompt Reference

Create a coordinate system showing multiple parabolas, each defined by two randomly chosen real rootsasi. Some parabolas open upward and some downward to illustrate different quadratic inequalities. On the number line, highlight the solution intervals for each inequality in distinct colors, with interval endpoints aligned to the parabola roots. Include a results table listing each inequality and its solution set. Ensure roots are unique across functions, with some functions constructed using opposite roots for symmetry. The overall layout should clearly connect each parabola's graph to its corresponding solution interval on the number line.
The prompt above was compiled from the original drawing commands and is for reference only.