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Solving Quadratic Equations with Mapping Diagrams (Real and Complex)

Solving Quadratic Equations with Mapping Diagrams (Real and Complex)
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2018-02-16 14:07
FunctionComplex NumberGraphing
This example uses mapping diagrams to solve quadratic equations, including both real and complex solutions. Key mathematical concepts include the roots of quadratic equations and their correspondence in mapping diagrams. Using GeoGebra commands like If, Sequence, and Zip, the example dynamically illustrates the properties of the solutions. Suitable for high school mathematics education and learning quadratic equation solutions.

GeoGebra Commands & Parameters

  1. If(RorC ≟ 2, w_C, w_R) → w
  2. If(RorC ≟ 2, k_C, k_R) → k
  3. If(RorC ≟ 2, h_C, h_R) → h
  4. If(RorC ≟ 2, A_C, A_R) → A
  5. Sequence(0, n) → M_1
  6. Zip(((2 * π) * k / n), k, M_1) → t_*
  7. Zip((δ * ℯ^((t * ί))) + z_#, t, t_*) → z_c
  8. Zip(z_# + ((t - π) * (P_l - z_#)), t, t_*) → z_l
  9. Line(z_#, P_l) → l
  10. Circle(z_#, δ) → c
  11. Point(c) → Pc
  12. If(m ≟ 1, z_c, z_l) → z_*
  13. Zip(s1(z), z, z_*) → fz_*
  14. Line(O, ZY1) → Im_{axis}
  15. Line(O, ZX1) → Real_{axis}
  16. Vector(z_#, fz1_#) → vecf_#
  17. Textfield(F) → InputBox1
  18. Zip((x(z), y(z), ht), z, fz_*) → fpt_*
  19. Zip(Vector[z, w], z, z_*, w, fpt_*) → fvec_*
  20. Locus(Pts1Pc, Pc) → loc_c
  21. Point(l) → Pl
  22. Locus(Pts1Pl, Pl) → loc_l
  23. Line((x(O2), y(O2), z(O2)), Vector[(1, 0, 0)]) → Real_{axis2}
  24. Line((x(O2), y(O2), z(O2)), Vector[(0, 1, 0)]) → Im_{axis2}
  25. Zip(g(s1(z)), z, z_*) → gfz_*
  26. Zip((x(z), y(z), (2 * ht)), z, gfz_*) → gfpt_*
  27. Zip(Vector[z, w], z, fpt_*, w, gfpt_*) → gfvec_*
  28. Locus(Ptgs1Pc, Pc) → loc2_c
  29. Textfield(G) → InputBox2
  30. Sequence(n_p) → Np
  31. Zip(z = (ht * k), k, Np) → Planes
  32. Zip(mf(g(s1(z))), z, z_*) → Agfz_*
  33. Zip((x(z), y(z), (3 * ht)), z, Agfz_*) → Agfpt_*
  34. Zip(Vector[z, w], z, gfpt_*, w, Agfpt_*) → Agfvec_*
  35. Zip(s2(mf(SQ(s1(z)))), z, z_*) → kAgfz_*
  36. Zip((x(z), y(z), (4 * ht)), z, kAgfz_*) → kAgfpt_*
  37. Zip(Vector[z, w], z, Agfpt_*, w, kAgfpt_*) → kAgfvec_*
  38. Locus(PtAgs1Pc, Pc) → Loc3_c
  39. Locus(Pts2Ags1Pc, Pc) → Loc4_c
  40. Locus(Ptgs1Pl, Pl) → loc2_l
  41. Locus(PtAgs1Pl, Pl) → Loc3_l
  42. Locus(Pts2Ags1Pl, Pl) → Loc4_l
  43. Vector(B3, Is2B3) → u
  44. Vector(Is2B3, IAIs2B3) → v
  45. Vector(IAIs2B3, SQRNIAIs2B3) → b
  46. Vector(SQRPIAIs2B3, Is1SQRPIAIs2B) → e
  47. Vector(SQRNIAIs2B3, Is1SQRNIAIs2B) → d
  48. Point(Planes) → B
  49. Vector(IAIs2B3, SQRPIAIs2B3) → a
  50. Zip((0, 0, (ht * k)), k, Np) → Os
  51. Zip(Line[p, Vector[(1, 0, 0)]], p, Os) → Axesx
  52. Zip(Line[p, Vector[(0, 1, 0)]], p, Os) → Axesy