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Completing the Square by Jill Vincent

Completing the Square by Jill Vincent
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2013-06-20 07:23
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the process of completing the square with simple quadratic expressions. Key mathematical concepts include quadratic expressions. The construction uses Polygon, Intersect, Vector, Midpoint, and other GeoGebra commands. Suitable for middle school and above students to learn the method of completing the square.

GeoGebra Commands & Parameters

  1. Polygon(B, D, C, A) → poly1, b_1, d, c_2, a
  2. Polygon(D, F, E, C) → poly2, d_1, f, e, c_1
  3. Polygon(G, I, D, B) → poly3, g, i, d_2, b_2
  4. Polygon(J, T, A_1, D) → poly4, j, t, a_1, d_3
  5. Polygon(B_1, Q, T, J) → poly5, b_3, q, t_1, j_1
  6. Polygon(K, P, Q, B_1) → poly6, k, p, q_1, b_4
  7. Polygon(Z_1, W_1, M, L) → poly8, z_1, w_1, m_1, l_1
  8. Polygon(A_2, B_2, W_1, Z_1) → poly9, a_2, b_5, w_2, z_2
  9. Polygon(Q, R, S, T) → poly10, q_2, r, s, t_2
  10. Polygon(T, S, J_2, A_1) → poly11, t_3, s_1, j_2, a_3
  11. Polygon(P, O, R, Q) → poly12, p_2, o, r_1, q_3
  12. Polygon(S, U, K_2, J_2) → poly13, s_2, u, k_2, j_3
  13. Polygon(R, V, U, S) → poly14, r_2, v, u_1, s_3
  14. Polygon(O, W, V, R) → poly15, o_1, w, v_1, r_3
  15. Polygon(L, M, P, K) → poly16, l_2, m_2, p_3, k_3
  16. Polygon(M, N, O, P) → poly17, m_3, n, o_2, p_4
  17. Polygon(N, Z, W, O) → poly18, n_1, z, w_3, o_3
  18. Polygon(Z, K_1, J_1, W) → poly19, z_3, k_4, j_4, w_4
  19. Polygon(W, J_1, I_1, V) → poly20, w_5, j_5, i_1, v_2
  20. Polygon(V, I_1, H_1, U) → poly21, v_3, i_2, h_1, u_2
  21. Polygon(U, H_1, C_1, K_2) → poly22, u_3, h_2, c_3, k_5
  22. Polygon(W_1, V_1, N, M) → poly7, w_6, v_4, n_2, m
  23. Polygon(V_1, U_1, Z, N) → poly23, v_5, u_4, z_4, n_3
  24. Polygon(U_1, T_1, K_1, Z) → poly24, u_5, t_4, k_1, z_5
  25. Polygon(H_1, G_1, D_1, C_1) → poly25, h_3, g_1, d_4, c_4
  26. Polygon(I_1, N_1, G_1, H_1) → poly26, i_3, n_4, g_2, h_4
  27. Polygon(J_1, M_1, N_1, I_1) → poly27, j_6, m_4, n_5, i_4
  28. Polygon(K_1, L_1, M_1, J_1) → poly28, k_6, l_3, m_5, j_7
  29. Polygon(T_1, S_1, L_1, K_1) → poly29, t_5, s_4, l_4, k_7
  30. Polygon(B_2, C_2, V_1, W_1) → poly30, b_6, c_5, v_6, w_7
  31. Polygon(C_2, D_2, U_1, V_1) → poly31, c_6, d_5, u_6, v_7
  32. Polygon(D_2, E_2, T_1, U_1) → poly32, d_6, e_2, t_6, u_7
  33. Polygon(E_2, F_2, S_1, T_1) → poly33, e_1, f_2, s_5, t_7
  34. Polygon(G_1, F_1, E_1, D_1) → poly34, g_3, f_1, e_3, d_7
  35. Polygon(N_1, O_1, F_1, G_1) → poly35, n_6, o_4, f_3, g_4
  36. Polygon(M_1, P_1, O_1, N_1) → poly36, m_6, p_1, o_5, n_7
  37. Polygon(L_1, Q_1, P_1, M_1) → poly37, l_5, q_4, p_5, m_7
  38. Polygon(S_1, R_1, Q_1, L_1) → poly38, s_6, r_4, q_5, l_6
  39. Polygon(F_2, G_2, R_1, S_1) → poly39, f_4, g_5, r_5, s_7
  40. Intersect(a, c_2) → H
  41. Intersect(b_2, g) → H_2
  42. Intersect(g_5, f_4) → L_2
  43. Intersect(e, f) → M_2
  44. Polygon(H, O_2, P_2, N_2) → poly40, h, o_6, p_6, n_8
  45. Vector(U_2, V_2) → l
  46. Vector(V_2, U_2) → a_4
  47. Midpoint(U_2, V_2) → W_2
  48. Vector(A_3, Z_2) → e_4
  49. Vector(Z_2, A_3) → a_5
  50. Midpoint(A_3, Z_2) → B_3

AI Drawing Prompt Reference

Draw a complex geometric structure consisting of multiple quadrilaterals and vectors. Start by drawing a quadrilateral with vertices at H, O2, P2, and N2. Then add other quadrilaterals and vectors, ensuring that each quadrilateral's vertices are correctly connected to the vectors, forming a intricate geometric shape.
The prompt above was compiled from the original drawing commands and is for reference only.