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Bisection Method to Find Real Roots of an Equation by Zero Neto

Bisection Method to Find Real Roots of an Equation by Zero Neto
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2019-04-12 12:16
FunctionCalculus
This example demonstrates the bisection method for finding real roots of an equation. Key mathematical concepts include functions, intervals, midpoints, and iteration. Using GeoGebra commands such as Point, Line, Intersect, etc., the process of the bisection method is dynamically illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. SelectedElement(Function) → f
  4. If((B2 * D2) < 0, true, false) → G2
  5. If(G2, A2, C2) → A3
  6. If(G2, C2, E2) → E3
  7. If((B3 * D3) < 0, true, false) → G3
  8. If(G3, A3, C3) → A4
  9. If(G3, C3, E3) → E4
  10. If((B4 * D4) < 0, true, false) → G4
  11. If(G4, A4, C4) → A5
  12. If(G4, C4, E4) → E5
  13. If((B5 * D5) < 0, true, false) → G5
  14. If(G5, A5, C5) → A6
  15. If(G5, C5, E5) → E6
  16. If((B6 * D6) < 0, true, false) → G6
  17. If(G6, A6, C6) → A7
  18. If(G6, C6, E6) → E7
  19. If((B7 * D7) < 0, true, false) → G7
  20. If(G7, A7, C7) → A8
  21. If(G7, C7, E7) → E8
  22. If((B8 * D8) < 0, true, false) → G8
  23. If(G8, A8, C8) → A9
  24. If(G8, C8, E8) → E9
  25. If((B9 * D9) < 0, true, false) → G9
  26. If(G9, A9, C9) → A10
  27. If(G9, C9, E9) → E10
  28. If((B10 * D10) < 0, true, false) → G10
  29. If(G10, A10, C10) → A11
  30. If(G10, C10, E10) → E11
  31. If((B11 * D11) < 0, true, false) → G11
  32. If(G11, A11, C11) → A12
  33. If(G11, C11, E11) → E12
  34. If((B12 * D12) < 0, true, false) → G12
  35. If(G12, A12, C12) → A13
  36. If(G12, C12, E12) → E13
  37. If((B13 * D13) < 0, true, false) → G13
  38. If(G13, A13, C13) → A14
  39. If(G13, C13, E13) → E14
  40. If((B14 * D14) < 0, true, false) → G14
  41. If(G14, A14, C14) → A15
  42. If(G14, C14, E14) → E15
  43. If((B15 * D15) < 0, true, false) → G15
  44. If(G15, A15, C15) → A16
  45. If(G15, C15, E15) → E16
  46. If((B16 * D16) < 0, true, false) → G16
  47. If(G16, A16, C16) → A17
  48. If(G16, C16, E16) → E17
  49. If((B17 * D17) < 0, true, false) → G17
  50. If(G17, A17, C17) → A18
  51. If(G17, C17, E17) → E18
  52. If((B18 * D18) < 0, true, false) → G18
  53. If(G18, A18, C18) → A19
  54. If(G18, C18, E18) → E19
  55. If((B19 * D19) < 0, true, false) → G19
  56. If(G19, A19, C19) → A20
  57. If(G19, C19, E19) → E20
  58. If((B20 * D20) < 0, true, false) → G20
  59. Line(A, xAxis) → a
  60. Line(A, a) → b
  61. OrthogonalLine(A, b) → c
  62. OrthogonalLine(B, b) → d
  63. Intersect(f, c) → C
  64. Intersect(f, d) → D
  65. Segment(D, B) → g
  66. Text(f) → text2
  67. If(e > 0, text4, text1) → text5

AI Drawing Prompt Reference

Draw a function graph, define an interval [A, B], repeatedly find the midpoint within the interval, check the sign of the product between the midpoint and the endpoints, and narrow down the interval based on the sign change until a point near the zero is found. Draw the function curve f(x) and the midpoints and endpoints of the interval at each iteration.
The prompt above was compiled from the original drawing commands and is for reference only.