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Completing the Square Demo by David T

Completing the Square Demo by David T
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2013-08-31 09:54
FunctionCoordinate GeometryParametric EquationGeometric Construction
This example demonstrates the geometric process of transforming a quadratic function into vertex form through completing the square. It involves core math concepts like quadratic functions, completing the square, vertex form, and geometric transformations. The construction utilizes GeoGebra commands and objects such as Polygon, Intersect, Vector, and Midpoint. Suitable for high school mathematics teaching to help students visually understand the geometric meaning and application 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
  51. Polygon(H_3, J_3, 4) → poly41, h_5, j_8, f_5, i_5, K_3, L_3

AI Drawing Prompt Reference

Create a geometric illustration showing the transformation of a quadratic function into vertex form via completing the square. Include multiple polygons, constructed through intersections and vectors, highlighting the vertex, axis of symmetry, and the function's graph. Start with basic polygons and build up to a complex structure that visually demonstrates the geometric meaning of completing the square.
The prompt above was compiled from the original drawing commands and is for reference only.