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二次项因式分解面积模型

二次项因式分解面积模型
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2015-06-14 01:39
函数三角函数几何作图滑块动画
①本范例演示用面积模型分解二次项，通过滑块找到给定二次项的两个因子；②涉及核心数学概念为二次函数因式分解、面积模型；③构造要点：使用 GeoGebra 命令 LeftSum, Sequence, Text, Simplify, Vector, VerticalText, 对象 a, b, c, d, width, RectXX, RectY, RectX, Rect1, text2, text5, text3, text4, f1, f2, f, A, B, e, u, text6, C, D, v, w, text7, t, NewProbButton, text8, count, CheckAnswerVisible, button2, text9, CheckVisible, score, correct, text10, text1；④适合初中及以上学生学习二次函数因式分解及面积模型应用。

GeoGebra 命令及参数

  1. LeftSum(width, 0, width, 1) → RectXX
  2. LeftSum(width, width, width + d, d) → RectY
  3. Sequence(Polygon[(0, width + i), (width, width + i), (width, width + 1 + i), (0, width + 1 + i)], i, 0, b - 1) → RectX
  4. Sequence(Sequence[Polygon[(width + j, width + i), (width + j + 1, width + i), (width + j + 1, width + 1 + i), (width + j, width + 1 + i)], i, 0, b - 1], j, 0, d - 1) → Rect1
  5. Text(x^(2), (width / 2 - 0.3, width / 2 - 0.3)) → text2
  6. Sequence(Text[x, (width / 2 - 0.2, width + 0.2 + i)], i, 0, b - 1) → text5
  7. Sequence(Text[x, (width + 0.3 + i, width / 2 - 0.3)], i, 0, d - 1) → text3
  8. Sequence(Sequence[Text[1, (width + 0.3 + i, width + 0.15 + j)], i, 0, d - 1], j, 0, b - 1) → text4
  9. Simplify((a * x) + b) → f1
  10. Simplify((c * x) + d) → f2
  11. Simplify((f1(x) * f2(x))) → f
  12. Vector(A, B) → e
  13. Vector(B, A) → u
  14. VerticalText(LaTeX[f1], ((-1.5), width / 2 + 1.7 + (b - 1) / 2 - Max[1 - b, 0] / 2)) → text6
  15. Vector(C, D) → v
  16. Vector(D, C) → w
  17. Text(LaTeX[f2], (width / 2 - 0.2 + Max[(d - 1) / 2, 0], (-1.3))) → text7
  18. Simplify(((x + Random[0, 5]) * (x + Random[0, 5]))) → t