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QR4-03-P4a-CYU2 二次函数图像绘制练习

QR4-03-P4a-CYU2 二次函数图像绘制练习
几何画板及绘图内容加载中，请稍等……
2018-12-02 08:11
多边形函数解析几何概率统计函数图像
① 本范例是一个交互式二次函数作图练习，学生需要在坐标平面上点击或输入点来绘制给定的二次函数图像，系统会实时判断所绘点是否正确。② 核心数学概念是二次函数的图像特征，包括顶点、对称轴、开口方向以及关键点的坐标确定，同时涉及概率与条件概率的反馈机制（如随机出题、尝试次数统计）。③ 作图要点：从构造摘要可见，使用了GeoGebra的Element、Flatten、Sequence、Point、UnicodeToLetter、LaTeX、FitPoly等命令，创建了用户点集userPts、正确点集correctPts、反馈点fbPoint、网格空间GridSpace、点空间PointSpace等对象，并通过条件判断isCorrect、showFeedback、TryAnother等实现交互反馈，背景中还有xmark、cmark等标记符号。④ 适合中学阶段（初中高年级或高中）学习二次函数图像的学生，也可用于教师课堂演示或学生自主练习，帮助巩固二次函数图像与坐标的关系。

GeoGebra 命令及参数

  1. Element(SolutionPtsLst, caseIndx) → correctPts
  2. Flatten(Sequence[Sequence[(i, j), i, -4, 4, 0.25], j, -4, 4, 0.25]) → GridSpace
  3. Sequence((i, y(fbPoint + 1.7)), i, x(fbPoint) + 2, x(fbPoint) + 4, 1) → PointSpace
  4. Point(Union[GridSpace, {Element[PointSpace, 1]}]) → P1
  5. Point(Union[GridSpace, {Element[PointSpace, 2]}]) → P2
  6. Point(Union[GridSpace, {Element[PointSpace, 3]}]) → P3
  7. UnicodeToLetter(10007) → xmark
  8. UnicodeToLetter(10003) → cmark
  9. LaTeX("\text{Points:}") → txtPointLbl
  10. LaTeX(chkUserInput) → fbCorrect
  11. LaTeX("\text{Plot all three points before \\checking your work.}") → fbNotDone
  12. LaTeX("\text{The three points you should plot are the \\two zeros and the vertex. Please try again.}") → fbTryAgain
  13. Point(GridSpace) → B2
  14. Point(GridSpace) → B3
  15. Point(GridSpace) → C2
  16. Point(GridSpace) → C3
  17. Point(GridSpace) → D2
  18. FitPoly(B2:B4, 2) → B5
  19. FitPoly(C2:C4, 2) → C5
  20. Point(GridSpace) → D3
  21. FitPoly(D2:D4, 2) → D5
  22. Point(GridSpace) → E2
  23. Point(GridSpace) → E3
  24. FitPoly(E2:E4, 2) → E5
  25. LaTeX("\Big(1,\dfrac{7}{4}\Big)") → B9
  26. Element(FunctionLst, caseIndx) → correctFunc
  27. Element(FunctionLst, caseIndx) → hintFunc
  28. Element(LatexValsLst, caseIndx) → CaseLatexVals
  29. LaTeX((("{\text{The vertex is } " * Element[CaseLatexVals, 2]) * ".")) → fbVertex
  30. LaTeX("x=1") → B12
  31. LaTeX("x=-1") → C12
  32. LaTeX("x=\dfrac{1}{4}") → E12
  33. LaTeX((("\text{The equation of the axis of symmetry is }" * Element[CaseLatexVals, 5]) * ".")) → fbAxisSym
  34. LaTeX("\Big(-1,-\dfrac{ 5}{4}\Big)") → C9
  35. LaTeX("\Big(-\dfrac{3}{4},3\Big)") → D9
  36. LaTeX("\Big(\dfrac{1}{4},-\dfrac{15}{4}\Big)") → E9
  37. LaTeX(If[A15 < 0, "-", ""]) → A21
  38. LaTeX(If[A15 ≟ 0, "0", If[A16 ≟ 0, "", ("" * A16)]]) → A22
  39. LaTeX(If[A17 ≟ 0, "", (((("\dfrac{" * A19) * "}{") * A20) * "}")]) → A23
  40. LaTeX(((("" * A21) * A22) * A23)) → A24
  41. LaTeX(If[B15 < 0, "-", ""]) → B21
  42. LaTeX(If[B15 ≟ 0, "0", If[B16 ≟ 0, "", ("" * B16)]]) → B22
  43. LaTeX(If[B17 ≟ 0, "", (((("\dfrac{" * B19) * "}{") * B20) * "}")]) → B23
  44. LaTeX(((("" * B21) * B22) * B23)) → B24
  45. LaTeX((((("\big(" * A24) * ",") * B24) * "\big)")) → lblActivePt
  46. LaTeX("x=-\dfrac{3}{4}") → D12
  47. LaTeX("x=-\dfrac{ 1}{2}") → B10
  48. LaTeX("x=-\dfrac{5}{2}") → C10
  49. LaTeX("x=-\dfrac{7}{4}") → D10
  50. LaTeX("x=-\dfrac{7}{2}") → E10
  51. LaTeX("x=\dfrac{5}{2}") → B11
  52. LaTeX("x-\dfrac{1}{2}") → C11
  53. LaTeX("x=\dfrac{1}{4}") → D11
  54. LaTeX("x=4") → E11
  55. LaTeX(((((" \text{The zeros occur at \(" * Element[CaseLatexVals, 3]) * "\) and \( ") * Element[CaseLatexVals, 4]) * "\).")) → fbZeros
  56. LaTeX((((("\text{\textbf{Question: }" * MainInstruc) * "\\\textbf{Instructions: }") * SpecInstruc) * "}")) → allInstruc