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Self-Assessment: Quadratic Function Graphs

Self-Assessment: Quadratic Function Graphs
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2017-06-19 11:22
FunctionCoordinate GeometryDerivativeOptimizationGraphing
This example demonstrates the plotting and transformation of quadratic function graphs, focusing on vertex, axis of symmetry, and direction of opening variations. Key math concepts include quadratic functions, vertex form (x-a)(x-b), symmetry, and coefficient effects. GeoGebra commands like Random, If, Shuffle, Coefficients, Element, Sequence, Polygon, Defined, Min, Max are used to dynamically generate and adjust function parameters. Suitable for high school mathematics teaching, enabling students to explore the properties of quadratic function graphs and parameter relationships independently.

GeoGebra Commands & Parameters

  1. Random(1, 4) → d
  2. Random(2, 4) → e'
  3. If(d ≟ e' ∧ (count > 7 ∨ count < 5), 1, e') → e
  4. Shuffle({2, 6, 7, 8}) → listshowFf2b, {8, 6, 2, 7}
  5. Shuffle({1, 4, 5, 8}) → listshowFf2a, {5, 4, 1, 8}
  6. Shuffle({1, 2, 3, 4}) → listshowFf1, {3, 4, 1, 2}
  7. If(count < 4, Element[listFf, Element[listshowFf1, 2]], If[count < 8, Element[listFf, Element[listshowFf2a, 2]], Element[listFf, Element[listshowFf2b, 2]]]) → f_{2s}
  8. Random(1, 4) → n_f
  9. Coefficients(f_{2s}) → listf_{2s}
  10. If(count < 4, Element[listFf, Element[listshowFf1, 1]], If[count < 8, Element[listFf, Element[listshowFf2a, 1]], Element[listFf, Element[listshowFf2b, 1]]]) → f_{1s}
  11. If(count < 4, Element[listFf, Element[listshowFf1, 4]], If[count < 8, Element[listFf, Element[listshowFf2a, 4]], Element[listFf, Element[listshowFf2b, 4]]]) → f_{4s}
  12. Coefficients(f_{1s}) → listf_{1s}
  13. Coefficients(f_{4s}) → listf_{4s}
  14. If(count < 4, Element[listFf, Element[listshowFf1, 3]], If[count < 8, Element[listFf, Element[listshowFf2a, 3]], Element[listFf, Element[listshowFf2b, 3]]]) → f_{3s}
  15. Coefficients(f_{3s}) → listf_{3s}
  16. Element(listCoeffs, n_f, 2) → b_f
  17. Element(listCoeffs, n_f, 1) → a_f
  18. Sequence(Sequence[(x(A) + (s_p * i), y(A) + (s_p * j)), i, 0, 3], j, 0, 0) → list3CtrofGraphs, {{(5, 0), (13.8, 0), (22.6, 0), (31.400000000000002, 0)}}
  19. Polygon(E, D, F, G) → poly2, e_1, d_1, f_5, g
  20. Polygon(G, F, H, I) → poly3, g_1, f_6, h, i
  21. Polygon(J, K, L, M) → poly4, j, k, l, m
  22. Polygon(J, K, C, B) → poly5, j_1, k_1, c, b_1
  23. Sequence(Sequence[Segment[(x(A) + (s_p * i) - l_x / 2, y(A) + (s_p * j)), (x(A) + (s_p * i) + l_x / 2, y(A) + (s_p * j))], i, 0, 3], j, 0, 0) → list1Xaxes, {{7.6000000000000005, 7.600000000000001, 7.600000000000001, 7.600000000000001}}
  24. Sequence(Sequence[Segment[(x(A) + (s_p * i), y(A) + (s_p * j) - l_y / 2), (x(A) + (s_p * i), y(A) + (s_p * j) + l_y / 2)], i, 0, 3], j, 0, 0) → list2Yaxes, {{9.2, 9.2, 9.2, 9.2}}
  25. Sequence(Sequence[(x(A) + l_x / 2 + (s_p * i), y(A) + (s_p * j)), i, 0, 3], j, 0, 0) → listXarrow, {{(8.8, 0), (17.6, 0), (26.400000000000002, 0), (35.2, 0)}}
  26. Sequence(Sequence[(x(A) + (s_p * i), y(A) + l_y / 2 + (s_p * j)), i, 0, 3], j, 0, 0) → listYarrow, {{(5, 4.6), (13.8, 4.6), (22.6, 4.6), (31.400000000000002, 4.6)}}
  27. Sequence(Sequence[Text[Element[listChoicestext, i + 1], (x(A) - l_x / 2 + (s_p * (i - 1)), y(A) + l_y / 2)], i, 1, 4], j, 0, 0) → listChoicestextDisplay, {{"(a)", "(b)", "(c)", "(d)"}}
  28. Element(listCoeffs, n_f, 3) → c_f
  29. Defined(root1) → realroots
  30. If(count < 4, Element[listFf, Element[listshowFf1, 4]], If[count < 8, Element[listFf, Element[listshowFf2a, 4]], Element[listFf, Element[listshowFf2b, 4]]]) → f_{tests}
  31. Polygon(B, C, D, E) → poly1, b, c_1, d_2, e_2
  32. If(count < 5, Element[listshowFf1, n_f], If[count < 9, Element[listshowFf2a, n_f], Element[listshowFf2b, n_f]]) → n_s
  33. Sequence(If[count < 4, Element[listshowFf1, i], If[count < 8, Element[listshowFf2a, i], Element[listshowFf2b, i]]], i, 1, 4) → listns
  34. Sequence({Cell[9, Element[listns, i]], Cell[10, Element[listns, i]]}, i, 1, 4) → listfsroots
  35. Sequence(Sequence[(((Element[listfsroots, i, j] * 2) * f_s) + x(A) + (s_p * (i - 1)), y(A)), j, 1, 2], i, 1, 4) → listfsxinttrans, {{(3.8, 0), (5.8, 0)}, {(12.600000000000001, 0), (13, 0)}, {(23.400000000000002, 0), (23.8, 0)}, {(30.6, 0), (32.6, 0)}}
  36. Min(d, e) → I1
  37. Min((-d), e) → I2
  38. Min(d, (-e)) → I3
  39. Min((-d), (-e)) → I4
  40. Min(d, e) → I5
  41. Min((-d), e) → I6
  42. Min(d, (-e)) → I7
  43. Min((-d), (-e)) → I8
  44. Max(d, e) → J1
  45. Max((-d), e) → J2
  46. Max((-d), e) → J6
  47. Max(d, (-e)) → J7
  48. Max(d, (-e)) → J3
  49. Max((-d), (-e)) → J4
  50. Max(d, e) → J5
  51. Max((-d), (-e)) → J8
  52. Element(listTurningPoints, n_f) → T_{do}
  53. Sequence(Sequence[(Element[listfsroots, i, j], y(A)), j, 1, 2], i, 1, 4) → listfsxintbeforetrans, {{(-3, 0), (2, 0)}, {(-3, 0), (-2, 0)}, {(2, 0), (3, 0)}, {(-2, 0), (3, 0)}}
  54. Element(listfsxintbeforetrans, n_f, 1) → R_{1o}
  55. Element(listfsxintbeforetrans, n_f, 2) → R_{2o}
  56. Element(listfsxinttrans, n_f, 1) → R_{1}
  57. Element(listfsxinttrans, n_f, 2) → R_{2}
  58. Element(listfYint, n_f) → Y_{into}