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QR4-03-P4a-CYU2 Graphing Quadratics

QR4-03-P4a-CYU2 Graphing Quadratics
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2018-12-02 08:11
PolygonFunctionCoordinate GeometryProbability & StatisticsGraphing
① This interactive example is a graphing quadratics exercise where students plot points on a coordinate plane to construct the graph of a quadratic function, with immediate feedback on correctness. ② Core math concepts include the graph of quadratic functions—vertex, axis of symmetry, direction of opening—and determining key coordinates, while also incorporating probability and conditional probability in the feedback system (random problem generation, attempt counting). ③ Construction highlights: from the summary, GeoGebra commands such as Element, Flatten, Sequence, Point, UnicodeToLetter, LaTeX, and FitPoly are used; objects include userPts, correctPts, fbPoint, GridSpace, PointSpace, P1/P2/P3, and interactive controls like isCorrect, showFeedback, TryAnother, with visual markers xmark and cmark. ④ Suitable for middle or high school students learning quadratic functions, and useful for classroom demonstration or self-paced practice to reinforce the relationship between quadratic equations and their graphs.

GeoGebra Commands & Parameters

  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