Completing the Square for Quadratic Functions

GeoGebra Commands & Parameters

1. Segment(A, B) → f
2. Segment(D, C) → h
3. Segment(C, A) → i
4. Polygon(A, B, D, C) → poly1, a_1, b_1, d, c
5. Sequence((a + i, 0), i, 0, abs(b / 2), 1) → bottoms
6. Sequence((a + i, a), i, 0, abs(b / 2), 1) → tops
7. Sequence((0, a + i), i, 0, abs(b / 2), 1) → lefts
8. Sequence((a, a + i), i, 0, abs(b / 2), 1) → rights
9. Sequence(Dilate[Element[bottoms, i], If[0 < g ≤ 1, 1 - g, 0], Element[tops, i]], i, 0, abs(b / 2) + 1, 1) → bottomsmove
10. Sequence(Dilate[Element[lefts, i], If[1 < g ≤ 2, 2 - g, 0], Element[rights, i]], i, 0, abs(b / 2) + 1, 1) → leftsmove
11. Point(bottomsmove) → E
12. Segment(B, E) → j
13. Dilate(C, If[1 < g ≤ 2, 2 - g, 0], D) → C'
14. Segment(C, C') → k
15. Polygon(D, H, F, G) → poly2, d_1, h_1, f_1, g_1
16. Dilate(H, If[2 < g ≤ 3, 3 - g, 0], F) → H'
17. Dilate(G, If[2 < g ≤ 3, 3 - g, 0], F) → G'
18. Dilate(I, If[2 < g ≤ 3, 3 - g, 0], A) → I'
19. Segment(I, I') → l
20. Rotate(I, If[3 < g ≤ 4, ((-(g - 3)) * π / 2), ((-π)) / 2], A) → I'_1
21. Rotate(I', If[3 < g ≤ 4, ((-(g - 3)) * π / 2), ((-π)) / 2], A) → I''
22. Segment(I'_1, I'') → l'
23. Rotate(I'_1, If[4 < g ≤ 5, ((-(g - 4)) * π / 2), ((-π)) / 2], I'_1) → J
24. Rotate(I'', If[4 < g ≤ 5, ((-(g - 4)) * π / 2), ((-π)) / 2], I'_1) → I'''
25. Segment(J, I''') → l''
26. Dilate(A, If[5 < g ≤ 6, 6 - g, 0], I) → A'
27. Vector(A, A') → u
28. Translate(I'_1, u) → K
29. Translate(I'', u) → I'''_1
30. Segment(K, I'''_1) → l''_1
31. Sequence(Segment[Element[bottoms, i + 1], Element[bottomsmove, i + 2]], i, 1, abs(b / 2), 1) → list1
32. Sequence(Segment[Element[lefts, i + 1], Element[leftsmove, i + 2]], i, 1, abs(b / 2), 1) → list2
33. Sequence(Polygon[Element[bottoms, i], Element[bottoms, i + 1], Element[tops, i + 1], Element[tops, i]], i, 1, abs(b / 2), 1) → list3
34. Sequence(Polygon[Element[lefts, i], Element[lefts, i + 1], Element[rights, i + 1], Element[rights, i]], i, 1, abs(b / 2), 1) → list4
35. Distance(D, F) → distanceDF
36. Textfield(b) → InputBox1