二次函数的顶点形式

二次函数的顶点形式
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2022-06-10 22:41
本范例演示二次函数的顶点形式。涉及的核心数学概念包括二次函数的性质和变换。通过使用GeoGebra命令如Polygon, Intersect, Vector, Midpoint, Translate, Segment等,可以动态展示二次函数的图像变换。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Polygon(B, D, C, A) → poly1, b_1, d, c_2, b_7
  2. Polygon(D, F, E, C) → poly2, d_1, f, f_5, c_1
  3. Polygon(G, I, D, B) → poly3, g, i, d_2, b_2
  4. Polygon(J, T, A_1, D) → p1, j, t_5, b_8, d_3
  5. Polygon(B_1, Q, T, J) → p2, b_3, q, t_1, j_1
  6. Polygon(K, P, Q, B_1) → p5, k, q_6, q_1, b_4
  7. Polygon(Z_1, W_1, M, L) → p17, z_1, w_1, m_1, l_1
  8. Polygon(A_2, B_2, W_1, Z_1) → p26, b_9, b_5, w_2, z_2
  9. Polygon(Q, R, S, T) → p4, q_2, r, s, t_2
  10. Polygon(T, S, J_2, A_1) → p3, t_3, s_1, j_2, c_7
  11. Polygon(P, O, R, Q) → p6, q_8, o, r_1, q_3
  12. Polygon(S, U, K_2, J_2) → p7, s_2, u, k_2, j_3
  13. Polygon(R, V, U, S) → p8, r_2, v, u_1, s_3
  14. Polygon(O, W, V, R) → p9, o_1, w, v_1, r_3
  15. Polygon(L, M, P, K) → p10, l_2, m_2, q_9, k_3
  16. Polygon(M, N, O, P) → p11, m_3, n, o_2, q_{10}
  17. Polygon(N, Z, W, O) → p12, n_1, z, w_3, o_3
  18. Polygon(Z, K_1, J_1, W) → p16, z_3, k_4, j_4, w_4
  19. Polygon(W, J_1, I_1, V) → p15, w_5, j_5, i_1, v_2
  20. Polygon(V, I_1, H_1, U) → p14, v_3, i_2, h_1, u_2
  21. Polygon(U, H_1, C_1, K_2) → p13, u_3, h_2, c_3, k_5
  22. Polygon(W_1, V_1, N, M) → p18, w_6, v_4, n_2, m
  23. Polygon(V_1, U_1, Z, N) → p19, v_5, u_4, z_4, n_3
  24. Polygon(H_1, G_1, D_1, C_1) → p21, h_3, g_1, d_4, c_4
  25. Polygon(I_1, N_1, G_1, H_1) → p22, i_3, n_4, g_2, h_4
  26. Polygon(J_1, M_1, N_1, I_1) → p23, j_6, m_4, n_5, i_4
  27. Polygon(K_1, L_1, M_1, J_1) → p24, k_6, l_3, m_5, j_7
  28. Polygon(T_1, S_1, L_1, K_1) → p25, t_9, s_4, l_4, k_7
  29. Polygon(B_2, C_2, V_1, W_1) → p27, b_6, c_5, v_6, w_7
  30. Polygon(C_2, D_2, U_1, V_1) → p28, c_6, d_5, u_6, v_7
  31. Polygon(D_2, E_2, T_1, U_1) → p29, d_6, f_7, t_6, u_7
  32. Polygon(E_2, F_2, S_1, T_1) → p30, f_6, f_2, s_5, t_7
  33. Polygon(G_1, F_1, E_1, D_1) → p31, g_3, f_1, f_8, d_7
  34. Polygon(N_1, O_1, F_1, G_1) → p32, n_6, o_4, f_3, g_4
  35. Polygon(M_1, P_1, O_1, N_1) → p33, m_6, q_7, o_5, n_7
  36. Polygon(L_1, Q_1, P_1, M_1) → p34, l_5, q_4, p_5, m_7
  37. Polygon(S_1, R_1, Q_1, L_1) → p35, s_6, r_4, q_5, l_6
  38. Polygon(F_2, G_2, R_1, S_1) → p36, f_4, g_5, r_5, s_7
  39. Intersect(b_7, c_2) → H
  40. Intersect(b_2, g) → H_2
  41. Intersect(g_5, f_4) → L_2
  42. Intersect(f_5, f) → M_2
  43. Vector(U_2, V_2) → l
  44. Midpoint(U_2, V_2) → W_2
  45. Midpoint(A_3, Z_2) → B_3
  46. Vector((0, 0), (0, -0.2)) → f_9
  47. Translate(W_2, f_9) → C_3
  48. Polygon(T_1, U_1, Z, K_1) → p20, t_8, u_5, z_5, k_8
  49. Segment(K_1, L_1) → p
  50. Segment(T_1, K_1) → z_{6}
  51. Vector(A_3, Z_2) → a
  52. Vector(Z_2, A_3) → e
  53. Vector(V_2, U_2) → a_1
  54. Segment(F, N_2) → p_6
  55. Segment(S_1, L_1) → h
  56. Segment(F, A_{100}) → p_1
  57. Segment(I, A_{100}) → k_1

AI 绘图提示语参考

绘制一个展示二次函数顶点形式的图形,包含多个多边形和它们的交点,通过向量、中点和平移操作展示二次函数的变换。首先画出基础的多边形,然后计算它们的交点,接着用向量和中点确定关键位置,最后通过平移操作展示二次函数的变换过程,整体呈现二次函数的几何性质和变换关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。