Completing the Square Method in Quadratic Functions

GeoGebra Commands & Parameters

1. Point(yAxis) → D
2. Point(xAxis) → B
3. Midpoint(B, D) → M_{BD}
4. Vector(P_{xsquared}, M_{BD}) → u_1
5. RandomElement({-7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7}) → a
6. Random(-7, 7) → b
7. Random(1, 7) → c
8. Simplify((x - a)^(2) - c^(2)) → sl1
9. Simplify(y^(2) + b2 * y) → sr2
10. Simplify(-((x - a)^(2) - c^(2) - x^(2) - a2 * x)) → s3
11. Simplify(x^(2) + a2 * x) → s4
12. Simplify((x - a)^(2)) → sl5
13. Simplify((y - b)^(2)) → sr5
14. Simplify(x - h) → sl6
15. Intersect(xAxis, yAxis) → A
16. Polygon(A, B, C, D) → poly1, a_1, b_1, c_1, d_1
17. Point(xAxis) → E
18. Point(xAxis) → F
19. Polygon(E, F, G, H) → poly2, e_1, f_1, g_1, h_1
20. Polygon(I, J, K, L) → poly3, i_1, j_1, k_1, l_1
21. Polygon(M, N, O, P) → poly4, m_1, n_1, o_1, p_1
22. Dilate(M, h / a, O) → M'
23. Dilate(N, h / a, O) → N'
24. Dilate(O, h / a, O) → O'
25. Dilate(P, h / a, O) → P'
26. Polygon(M', N', O', P') → poly4', m', n', o', p'
27. Midpoint(A, B) → M_{AB}
28. Midpoint(A, D) → M_{AD}
29. Midpoint(E, F) → M_{EF}
30. Midpoint(F, H) → M_{FH}
31. Midpoint(I, L) → M_{IL}
32. Midpoint(J, L) → M_{JL}
33. Midpoint(N', P') → M_{NP}
34. Translate(P_{xsquared}, Vector[n_{motion} * u_1]) → R
35. Vector(P_{xsquared}, R) → v_1
36. Vector(P_{bx}, M_{FH}) → u_2
37. Translate(P_{bx}, Vector[n_{motion} * u_2]) → Q
38. Vector(P_{bx}, M_{JL}) → u_3
39. Translate(P_{bx}, Vector[n_{motion} * u_3]) → S
40. Vector(P_{bx}, Q) → v_2
41. Vector(P_{bx}, S) → v_3
42. Dilate(M, j / a^(2), O) → M'_1
43. Dilate(N, j / a^(2), O) → N'_1
44. Dilate(O, j / a^(2), O) → O'_1
45. Dilate(P, j / a^(2), O) → P'_1
46. Polygon(M'_1, N'_1, O'_1, P'_1) → poly4'_1, m'_1, n'_1, o'_1, p'_1