绝对值方程与不等式的几何演示

绝对值方程与不等式的几何演示
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2020-08-19 10:22
①本范例通过动态演示展示绝对值方程与不等式的几何意义,直观呈现解集与图形关系;②涉及核心数学概念包括绝对值函数、方程解、不等式区域、坐标几何;③构造中运用了RandomDiscrete, Vector, Segment, Random, DivisorsList, Factors, If, Max, Min, Textfield, RandomElement, Element, Line等GeoGebra命令与对象,实现随机生成与动态交互;④适合高中数学教学,用于理解绝对值函数的图像与性质,提升解析几何能力。

GeoGebra 命令及参数

  1. RandomDiscrete({1, 2, 3, 4, 5}, {2, 5, 5, 5, 5}) → whatweget
  2. Vector(C, D) → u
  3. Vector(E, F) → a
  4. Segment(G, H) → f
  5. Random(-60, 60) → K
  6. Random(-60, 60) → Qstart
  7. RandomDiscrete({Qstart, 0}, {8, 2}) → Q
  8. DivisorsList(abs(K - Q)) → Lpos
  9. Factors(abs(K - Q)) →
  10. If(K - Q > 0, Lpos, K - Q < 0, Lneg, RandomElement[{-3, -2, -1, 1, 2, 3, 4, 5}]) → Lwin
  11. If(K - Q < 0, Lpos, K - Q > 0, Lneg, RandomElement[{-3, -2, -1, 1, 2, 3, 4}]) → Lloss
  12. RandomDiscrete({RandomElement[Lwin], RandomElement[Lloss]}, {85, 15}) → L
  13. Random(-20, 20) → Pstart
  14. RandomDiscrete({Pstart, 0}, {8, 2}) → P
  15. RandomDiscrete({-10, 10, 8, -8, 5, -5, 4, -4, 3, -3, 2, -2, 1, -1}, {1, 1, 1, 1, 3, 2, 3, 2, 3, 2, 4, 3, 5, 2}) → M
  16. Max({x_{one}, x_{two}}) → ans_{1}
  17. Min({x_{one}, x_{two}}) → ans_{2}
  18. If((K - Q) / L ≥ 0, 1, (K - Q) / L < 0, 0) → Finish
  19. If(Finish ≟ 1, ans_{1}, Finish ≟ 0, NaN) → x_{1}
  20. If(Finish ≟ 1, ans_{2}, Finish ≟ 0, NaN) → x_{2}
  21. If(Finish ≟ 1, "yes", Finish ≟ 0, "no") → obvious
  22. Textfield(text4) → InputBox1
  23. Textfield(guess2) → InputBox2
  24. Textfield(guess1) → InputBox3
  25. RandomElement({1, 2, 3, 4}) → whatweget2
  26. Element({{equal1, equal2, equal3, equal4}, {GT1, GT2, GT3, GT4}, {LT1, LT2, LT3, LT4}, {GTE1, GTE2, GTE3, GTE4}, {LTE1, LTE2, LTE3, LTE4}}, whatweget, whatweget2) → whattheysee
  27. Textfield(multchoice) → InputBox4
  28. If(Finish ≟ 1 ∧ L > 0, 1, Finish ≟ 1 ∧ L < 0, 2, Finish ≟ 0 ∧ L > 0, 3, Finish ≟ 0 ∧ L < 0, 4) → flipsign
  29. Element({{"G", "G", "A", "A"}, {"D", "F", "A", "B"}, {"F", "D", "B", "A"}, {"C", "E", "A", "B"}, {"E", "C", "B", "A"}}, whatweget, flipsign) → multchoiceanswer
  30. Vector(LeftPt, (x_{2} - 5, 0)) → LeftVector
  31. Vector(RightPt, (x_{1} + 5, 0)) → RightVector
  32. Line(LeftPt, RightPt) → WholeLine
  33. Segment(LeftPt, RightPt) → Segment1
  34. If(whatweget ≟ 1, Element[{equal1, equal2, equal3, equal4}, whatweget2]) → whattheysee2

AI 绘图提示语参考

绘制绝对值方程和不等式的几何演示,展示随机生成的点和向量,通过坐标几何关系确定不等式的解集和图形表示,包括线段、区域和文本标注,最终呈现解集与图形的对应关系,适合高中数学教育理解绝对值函数的图形和性质。
以上提示语为根据原始绘图命令整理而来,仅供参考。