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Equations from Tables

Equations from Tables
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2015-02-06 01:22
FunctionSequenceCoordinate GeometryGraphing
This example demonstrates how to transform table data into linear function equations using GeoGebra. Core math concepts include equation representation, division, and linear functions. Construction highlights involve commands like Sequence, Sort, Random, Element, Join, FractionText, If, TableText, and objects such as button1, list2, list1, coefs, A1, startingX1, A2, intervalX1, A3, A4, A5, A6, coef1, A7, coef2, coef3, coef4, coef5, b2, b3, b4, b5, coef6, b, b6, b1, B2, B3, B4, B5, B6, B7, D1, startingX2, D2, intervalX2, D3, D4, D5, D6. Suitable for middle school and above students to understand the relationship between data and functions, and to master equation construction techniques.

GeoGebra Commands & Parameters

  1. Sequence(i, i, 1, 20) → list2
  2. Sequence((-i), i, 1, 20) → list1
  3. Sort(Join[{list1, list2}]) → coefs
  4. Random(0, 20) → startingX1
  5. Random(0, 10) → intervalX1
  6. Element(coefs, Random[1, 20]) → coef1
  7. Element(coefs, Random[1, 20]) → coef2
  8. Element(coefs, Random[1, 20]) → coef3
  9. Element(coefs, Random[1, 20]) → coef4
  10. Element(coefs, Random[1, 20]) → coef5
  11. Element(coefs, Random[1, 20]) → coef6
  12. Join({list1, list2, {0}}) → b
  13. FractionText((coef1 * A2^(2)) + b1) → B2
  14. FractionText((coef1 * A3^(2)) + b1) → B3
  15. FractionText((coef1 * A4^(2)) + b1) → B4
  16. FractionText((coef1 * A5^(2)) + b1) → B5
  17. FractionText((coef1 * A6^(2)) + b1) → B6
  18. FractionText((coef1 * A7^(2)) + b1) → B7
  19. Random(0, 20) → startingX2
  20. Random(0, 10) → intervalX2
  21. FractionText((coef2 * D2^(2)) + b2) → E2
  22. FractionText((coef2 * D3^(2)) + b2) → E3
  23. FractionText((coef2 * D4^(2)) + b2) → E4
  24. FractionText((coef2 * D5^(2)) + b2) → E5
  25. FractionText((coef2 * D6^(2)) + b2) → E6
  26. FractionText((coef2 * D7^(2)) + b2) → E7
  27. Random(0, 20) → startingX3
  28. Random(0, 10) → intervalX3
  29. FractionText((coef3 * G2^(2)) + b3) → H2
  30. FractionText((coef3 * G3^(2)) + b3) → H3
  31. FractionText((coef3 * G4^(2)) + b3) → H4
  32. FractionText((coef3 * G5^(2)) + b3) → H5
  33. FractionText((coef3 * G6^(2)) + b3) → H6
  34. FractionText((coef3 * G7^(2)) + b3) → H7
  35. Random(0, 20) → startingX4
  36. Random(0, 10) → intervalX4
  37. FractionText((coef4 * J2^(2)) + b4) → K2
  38. FractionText((coef4 * J3^(2)) + b4) → K3
  39. FractionText((coef4 * J4^(2)) + b4) → K4
  40. FractionText((coef4 * J5^(2)) + b4) → K5
  41. FractionText((coef4 * J6^(2)) + b4) → K6
  42. FractionText((coef4 * J7^(2)) + b4) → K7
  43. Random(0, 20) → startingX5
  44. Random(0, 10) → intervalX5
  45. FractionText((coef5 * M2^(2)) + b5) → N2
  46. FractionText((coef5 * M3^(2)) + b5) → N3
  47. FractionText((coef5 * M4^(2)) + b5) → N4
  48. FractionText((coef5 * M5^(2)) + b5) → N5
  49. FractionText((coef5 * M6^(2)) + b5) → N6
  50. FractionText((coef5 * M7^(2)) + b5) → N7
  51. Random(0, 20) → startingX6
  52. Random(0, 10) → intervalX6
  53. FractionText((coef6 * P2^(2)) + b6) → Q2
  54. FractionText((coef6 * P3^(2)) + b6) → Q3
  55. FractionText((coef6 * P4^(2)) + b6) → Q4
  56. FractionText((coef6 * P5^(2)) + b6) → Q5
  57. FractionText((coef6 * P6^(2)) + b6) → Q6
  58. FractionText((coef6 * P7^(2)) + b6) → Q7
  59. If(b1 < 0, (-b1), b1) → forTextb1
  60. If(b2 < 0, (-b2), b2) → forTextb2
  61. If(b3 < 0, (-b3), b3) → forTextb3
  62. If(b4 < 0, (-b4), b4) → forTextb4
  63. If(b5 < 0, (-b5), b5) → forTextb5
  64. If(b6 < 0, (-b6), b6) → forTextb6
  65. If(b1 < 0, " - ", " + ") → sign1
  66. If(b2 < 0, " - ", " + ") → sign2
  67. If(b3 < 0, " - ", " + ") → sign3
  68. If(b4 < 0, " - ", " + ") → sign4
  69. If(b5 < 0, " - ", " + ") → sign5
  70. If(b6 < 0, " - ", " + ") → sign6
  71. If(showAnswers ≟ true, (("y = " * coef1) * "x²"), "y") → yText1
  72. If(showAnswers ≟ true, (("y = " * coef2) * "x²"), "y") → yText2
  73. If(showAnswers ≟ true, (("y = " * coef3) * "x²"), "y") → yText3
  74. If(showAnswers ≟ true, (("y = " * coef4) * "x²"), "y") → yText4
  75. If(showAnswers ≟ true, (("y = " * coef5) * "x²"), "y") → yText5
  76. If(showAnswers ≟ true, (("y = " * coef6) * "x²"), "y") → yText6
  77. TableText({{A1, B1}, {A2, B2}, {A3, B3}, {A4, B4}, {A5, B5}, {A6, B6}, {A7, B7}}, "|_") → Table1
  78. TableText({{D1, E1}, {D2, E2}, {D3, E3}, {D4, E4}, {D5, E5}, {D6, E6}, {D7, E7}}, "|_") → Table2
  79. TableText({{G1, H1}, {G2, H2}, {G3, H3}, {G4, H4}, {G5, H5}, {G6, H6}, {G7, H7}}, "|_") → Table3
  80. TableText({{J1, K1}, {J2, K2}, {J3, K3}, {J4, K4}, {J5, K5}, {J6, K6}, {J7, K7}}, "|_") → Table4
  81. TableText({{M1, N1}, {M2, N2}, {M3, N3}, {M4, N4}, {M5, N5}, {M6, N6}, {M7, N7}}, "|_") → Table5
  82. TableText({{P1, Q1}, {P2, Q2}, {P3, Q3}, {P4, Q4}, {P5, Q5}, {P6, Q6}, {P7, Q7}}, "|_") → Table6

AI Drawing Prompt Reference

Create a graph showing how to transform table data into linear function equations. Generate two sets of symmetric data, sort them, and randomly select coefficients to form multiple linear function graphs. Each function is displayed in a different color with marked points, highlighting the relationship between the function images and data points to illustrate the construction process of function equations.
The prompt above was compiled from the original drawing commands and is for reference only.