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配方法入门 by Mark Beckwith

配方法入门 by Mark Beckwith
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2017-04-07 19:44
函数解析几何最值优化
①本范例演示通过动态图形展示配方法在二次函数中的应用，直观呈现顶点变换；②涉及核心数学概念包括二次函数、配方法、顶点坐标、函数图像变换；③构造要点提炼自GeoGebra命令：Polygon（多边形）、Distance（距离）、Perimeter（周长）、PointIn（点在图形内判断）、Textfield（文本框）；④适合初中及以上学生学习二次函数性质及配方法几何意义，也可用于数学教学演示。

GeoGebra 命令及参数

  1. Polygon(A, D, G, C) → poly1, a_1, d_1, g_1, c_1
  2. Polygon(A, E, F, B) → poly2, a_2, e, f_1, b_3
  3. Polygon(A, E, H, C) → poly3, a_3, e_1, h, c_2
  4. Polygon(H, G, I, F) → poly4, h_1, g_2, i, f_2
  5. Distance(A, C) → distanceAC
  6. Distance(A, E) → distanceAE
  7. Distance(A, H) → distanceAH
  8. Distance(E, D) → distanceED
  9. Distance(C, B) → distanceCB
  10. Distance(E, G) → distanceEG
  11. Distance(C, F) → distanceCF
  12. Distance(H, I) → distanceHI
  13. Polygon(A, J, K, L) → poly5, a_4, j_1, k, l
  14. Polygon(J, M, N, K) → poly6, j_2, m, n, k_1
  15. Polygon(J, M, N, K) → poly8, j_3, m_1, n_1, k_3
  16. Polygon(K, P, O, L) → poly7, k_2, p, o, l_1
  17. Polygon(K, P, O, L) → poly9, k_4, p_1, o_1, l_2
  18. Polygon(R, T, Q, S) → poly10, r_9, t, q_1, s
  19. Polygon(R, T, Q, S) → poly11, r_{10}, t_1, q_2, s_1
  20. Distance(A, U) → distanceAU
  21. Distance(A, V) → distanceAV
  22. Distance(A, R) → distanceAR
  23. Polygon(R, T, Q, S) → poly12, r_{11}, t_2, q_3, s_2
  24. Distance(R, Q) → distanceRQ
  25. Perimeter(poly12) → perimeterpoly12
  26. PointIn(poly12) → Pointpoly12
  27. Textfield(g_{10}) → InputBox1
  28. Textfield(g_{11}) → InputBox2