复根的二次方程（抛物线）

GeoGebra 命令及参数

1. Point({F_{x}, F_{y}}) → F
2. Line(F, yAxis) → f
3. Intersect(d, f) → B
4. OrthogonalLine(B, d) → i
5. Intersect(i, xAxis) → D
6. Line(D, yAxis) → l
7. Parabola(F, d) → c
8. Intersect(c, i) → T_{x},
9. OrthogonalLine(T_{x}, yAxis) → n
10. Intersect(n, yAxis) → V''
11. OrthogonalLine(T_{x}, xAxis) → j
12. Intersect(d, j) → H
13. OrthogonalLine(H, yAxis) → m
14. Intersect(m, yAxis) → F''
15. Distance(V'', F'') → fl''
16. OrthogonalLine(Point[{0, y(V'') - (sgn(y(F'') - y(V'')) * fl'')}], yAxis) → d''
17. Parabola(F'', d'') → c''
18. Intersect(c'', xAxis) → J, K
19. Line(Point[{0, x(J)}], xAxis) → r_{1}
20. Line(F, xAxis) → e
21. If(a ≠ 0, Intersect[d, e], Point[{Infinity, F_{x}}]) → A
22. OrthogonalLine(A, d) → h
23. If(a ≠ 0, Intersect[c, h], Point[{Infinity, Infinity}]) → T_{y}
24. Point({x(T_{y}), 0}) → F'
25. Point({x(T_{x}), 0}) → V'
26. Distance(V', F') → fl'
27. OrthogonalLine(Point[{x(V') - (sgn(x(F') - x(V')) * fl'), 0}], xAxis) → d'
28. If(a ≠ 0, Parabola[F', d'], f) → c'
29. OrthogonalLine(T_{y}, xAxis) → k
30. Intersect(k, xAxis) → E
31. Intersect(j, xAxis) → G
32. Segment(F, A) → s_{a}
33. Segment(A, T_{y}) → s_{c}
34. Segment(T_{y}, E) → s_{f}
35. Segment(F, B) → s_{b}
36. Segment(B, T_{x}) → s_{d}
37. Segment(T_{x}, G) → s_{e}
38. Point(c') → z_{1}
39. If(a ≟ 0, par0(z_{1}), If[imaginary(par1(z_{1})) ≟ 0, par1(z_{1}), par2(z_{1})]) → z'_{1}
40. Segment(B, D) → s_{g}
41. Intersect(r_{1}, l) → R_1
42. Segment(D, R_1) → s_{h}
43. Angle(d, h) → α
44. Angle(d, i) → β
45. Segment(T_{x}, Point[{0, y(T_{x})}]) → s_{j}
46. Point({imaginary(z_{1}), fr(imaginary(z_{1}))}) → z''_{1}
47. Segment(G, H) → s_{k}
48. Segment(H, F'') → s_{l}
49. Intersect(d, k) → I
50. Segment(I, V'') → s_{m}
51. Segment(I, F') → s_{n}
52. Segment(T_{x}, T_{y}) → s_{o}
53. CircleArc(Point[{0, 0}], Point[{0, (-x(J))}], Point[{0, x(J)}]) → p
54. Segment(Point[{0, x(J)}], R_1) → s_{p1}
55. Line(Point[{0, (-x(J))}], xAxis) → r_{2}
56. Intersect(r_{2}, l) → R_{2}
57. Segment(Point[{0, (-x(J))}], R_{2}) → s_{p2}
58. Segment(D, R_{2}) → s_{i}
59. Vertex(c) → V, , ,
60. FirstAxis(c) → g