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篮球框 #02 - 顶点形式的抛物线

篮球框 #02 - 顶点形式的抛物线
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2015-11-20 05:14
函数解析几何变换
本范例通过输入抛物线的顶点形式方程，使篮球穿过三个点：顶点和两个对称点。涉及的核心数学概念包括抛物线和特殊点。使用了构造摘要中的 GeoGebra 命令，如 Textfield, Corner, Line, Intersect, Rotate 等。适合初中及以上学生学习解析几何和抛物线的相关知识。

GeoGebra 命令及参数

  1. Textfield(f) → inputBox1
  2. Corner(1) → bottomLeftCorner
  3. Corner(2) → bottomRightCorner
  4. Line(bottomLeftCorner, bottomRightCorner) → bottomEdge
  5. Corner(4) → topLeftCorner
  6. Corner(3) → topRightCorner
  7. Line(topLeftCorner, topRightCorner) → upperEdge
  8. Intersect(f, bottomEdge) → M, N
  9. Intersect(f, upperEdge) → O, P
  10. Rotate(B_1, atan(g'(x(B))), B) → B_{1rot}
  11. Rotate(B_2, atan(g'(x(B))), B) → B_{2rot}
  12. Rotate(B_3, atan(g'(x(B))), B) → B_{3rot}
  13. Rotate(B_4, atan(g'(x(B))), B) → B_{4rot}
  14. Rotate(A_1, atan(g'(x(A))), A) → A_{1rot}
  15. Rotate(A_2, atan(g'(x(A))), A) → A_{2rot}
  16. Rotate(A_3, atan(g'(x(A))), A) → A_{3rot}
  17. Rotate(A_4, atan(g'(x(A))), A) → A_{4rot}
  18. Rotate(C_1, atan(g'(x(C))), C) → C_{1rot}
  19. Rotate(C_2, atan(g'(x(C))), C) → C_{2rot}
  20. Rotate(C_3, atan(g'(x(C))), C) → C_{3rot}
  21. Rotate(C_4, atan(g'(x(C))), C) → C_{4rot}