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二次函数图像自评

二次函数图像自评
几何画板及绘图内容加载中，请稍等……
2017-06-19 11:22
函数解析几何导数最值优化函数图像
所属专题 Self Assessment MCQs Collection
①本范例演示了二次函数图像的绘制与变换，特别是涉及顶点、对称轴及开口方向的变化；②核心数学概念包括二次函数、顶点式(x-a)(x-b)、对称性、系数影响；③作图要点运用了Random, If, Shuffle, Coefficients, Element, Sequence, Polygon, Defined, Min, Max等GeoGebra命令与对象，用于动态生成与调整函数参数；④适合高中数学教学，用于学生自主探究二次函数图像特性与参数关系。

GeoGebra 命令及参数

  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}