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Exponential Functions and Geometric Constructions

Exponential Functions and Geometric Constructions
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2017-05-05 09:28
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the intersection of exponential function graphs with geometric shapes like kites, involving concepts such as exponentials, polygons, tangent and secant lines, and quadratic equations. It uses GeoGebra commands like Intersect, Polygon, Point, and Distance for construction, suitable for high school mathematics education to explore the integration of functions and geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Polygon(A, B, C, D) → polyA6, a, b, c, d
  3. Point(yAxis) → F
  4. Polygon(D, C, E, F) → polyA5, d_1, c_1, e, f
  5. Point(yAxis) → H
  6. Polygon(F, E, G, H) → polyA4, f_1, e_1, g, h
  7. Point(yAxis) → J
  8. Polygon(J, I, K, L) → polyA2, j_1, i_1, k, l
  9. Polygon(L, K, M, N) → polyA1, l_1, k_1, m, n
  10. Polygon(B, O, P, C) → polyB6, b_1, o, p, c_2
  11. Polygon(C, P, Q, E) → polyB5, c_3, p_1, q, e_2
  12. Polygon(E, Q, R, G) → polyB4, e_3, q_1, r, g_2
  13. Polygon(G, R, S, I) → polyB3, g_3, r_1, s, i_2
  14. Polygon(I, S, T, K) → polyB2, i_3, s_1, t, k_2
  15. Polygon(K, T, U, M) → polyB1, k_3, t_1, u, m_1
  16. Point(xAxis) → V
  17. Polygon(O, V, W, P) → polyC6, o_1, v, w, p_2
  18. Polygon(P, W, Z, Q) → polyC5, p_3, w_1, z_1, q_2
  19. Polygon(Q, Z, A_1, R) → polyC4, q_3, z_2, a_1, r_2
  20. Polygon(R, A_1, B_1, S) → polyC3, r_3, a_2, b_2, s_2
  21. Polygon(S, B_1, C_1, T) → polyC2, s_3, b_3, c_4, t_2
  22. Polygon(T, C_1, D_1, U) → polyC1, t_3, c_5, d_2, u_1
  23. Point(xAxis) → E_1
  24. Polygon(V, E_1, F_1, W) → polyD6, v_1, e_4, f_2, w_2
  25. Polygon(W, F_1, G_1, Z) → polyD5, w_3, f_3, g_4, z_3
  26. Polygon(Z, G_1, H_1, A_1) → polyD4, z_4, g_5, h_2, a_3
  27. Polygon(A_1, H_1, I_1, B_1) → polyD3, a_4, h_3, i_4, b_4
  28. Polygon(B_1, I_1, J_1, C_1) → polyD2, b_5, i_5, j_2, c_6
  29. Polygon(C_1, J_1, K_1, D_1) → polyD1, c_7, j_3, k_4, d_3
  30. Point(xAxis) → L_1
  31. Polygon(E_1, L_1, M_1, F_1) → polyE6, e_5, l_2, m_2, f_4
  32. Polygon(F_1, M_1, N_1, G_1) → polyE5, f_5, m_3, n_1, g_6
  33. Polygon(G_1, N_1, O_1, H_1) → polyE4, g_7, n_2, o_2, h_4
  34. Polygon(H_1, O_1, P_1, I_1) → polyE3, h_5, o_3, p_4, i_6
  35. Polygon(I_1, P_1, Q_1, J_1) → polyE2, i_7, p_5, q_4, j_4
  36. Polygon(J_1, Q_1, R_1, K_1) → polyE1, j_5, q_5, r_4, k_5
  37. Point(xAxis) → S_1
  38. Polygon(L_1, S_1, T_1, M_1) → polyF6, l_3, s_4, t_4, m_4
  39. Polygon(M_1, T_1, U_1, N_1) → polyF5, m_5, t_5, u_2, n_3
  40. Polygon(N_1, U_1, V_1, O_1) → polyF4, n_4, u_3, v_2, o_4
  41. Polygon(O_1, V_1, W_1, P_1) → polyF3, o_5, v_3, w_4, p_6
  42. Polygon(P_1, W_1, Z_1, Q_1) → polyF2, p_7, w_5, z_5, q_6
  43. Polygon(Q_1, Z_1, A_2, R_1) → polyF1, q_7, z_6, a_5, r_5
  44. Distance(M, T) → MT