二次函数的顶点形式
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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
Polygon(B, D, C, A) → poly1, b_1, d, c_2, b_7Polygon(D, F, E, C) → poly2, d_1, f, f_5, c_1Polygon(G, I, D, B) → poly3, g, i, d_2, b_2Polygon(J, T, A_1, D) → p1, j, t_5, b_8, d_3Polygon(B_1, Q, T, J) → p2, b_3, q, t_1, j_1Polygon(K, P, Q, B_1) → p5, k, q_6, q_1, b_4Polygon(Z_1, W_1, M, L) → p17, z_1, w_1, m_1, l_1Polygon(A_2, B_2, W_1, Z_1) → p26, b_9, b_5, w_2, z_2Polygon(Q, R, S, T) → p4, q_2, r, s, t_2Polygon(T, S, J_2, A_1) → p3, t_3, s_1, j_2, c_7Polygon(P, O, R, Q) → p6, q_8, o, r_1, q_3Polygon(S, U, K_2, J_2) → p7, s_2, u, k_2, j_3Polygon(R, V, U, S) → p8, r_2, v, u_1, s_3Polygon(O, W, V, R) → p9, o_1, w, v_1, r_3Polygon(L, M, P, K) → p10, l_2, m_2, q_9, k_3Polygon(M, N, O, P) → p11, m_3, n, o_2, q_{10}Polygon(N, Z, W, O) → p12, n_1, z, w_3, o_3Polygon(Z, K_1, J_1, W) → p16, z_3, k_4, j_4, w_4Polygon(W, J_1, I_1, V) → p15, w_5, j_5, i_1, v_2Polygon(V, I_1, H_1, U) → p14, v_3, i_2, h_1, u_2Polygon(U, H_1, C_1, K_2) → p13, u_3, h_2, c_3, k_5Polygon(W_1, V_1, N, M) → p18, w_6, v_4, n_2, mPolygon(V_1, U_1, Z, N) → p19, v_5, u_4, z_4, n_3Polygon(H_1, G_1, D_1, C_1) → p21, h_3, g_1, d_4, c_4Polygon(I_1, N_1, G_1, H_1) → p22, i_3, n_4, g_2, h_4Polygon(J_1, M_1, N_1, I_1) → p23, j_6, m_4, n_5, i_4Polygon(K_1, L_1, M_1, J_1) → p24, k_6, l_3, m_5, j_7Polygon(T_1, S_1, L_1, K_1) → p25, t_9, s_4, l_4, k_7Polygon(B_2, C_2, V_1, W_1) → p27, b_6, c_5, v_6, w_7Polygon(C_2, D_2, U_1, V_1) → p28, c_6, d_5, u_6, v_7Polygon(D_2, E_2, T_1, U_1) → p29, d_6, f_7, t_6, u_7Polygon(E_2, F_2, S_1, T_1) → p30, f_6, f_2, s_5, t_7Polygon(G_1, F_1, E_1, D_1) → p31, g_3, f_1, f_8, d_7Polygon(N_1, O_1, F_1, G_1) → p32, n_6, o_4, f_3, g_4Polygon(M_1, P_1, O_1, N_1) → p33, m_6, q_7, o_5, n_7Polygon(L_1, Q_1, P_1, M_1) → p34, l_5, q_4, p_5, m_7Polygon(S_1, R_1, Q_1, L_1) → p35, s_6, r_4, q_5, l_6Polygon(F_2, G_2, R_1, S_1) → p36, f_4, g_5, r_5, s_7Intersect(b_7, c_2) → HIntersect(b_2, g) → H_2Intersect(g_5, f_4) → L_2Intersect(f_5, f) → M_2Vector(U_2, V_2) → lMidpoint(U_2, V_2) → W_2Midpoint(A_3, Z_2) → B_3Vector((0, 0), (0, -0.2)) → f_9Translate(W_2, f_9) → C_3Polygon(T_1, U_1, Z, K_1) → p20, t_8, u_5, z_5, k_8Segment(K_1, L_1) → pSegment(T_1, K_1) → z_{6}Vector(A_3, Z_2) → aVector(Z_2, A_3) → eVector(V_2, U_2) → a_1Segment(F, N_2) → p_6Segment(S_1, L_1) → hSegment(F, A_{100}) → p_1Segment(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。