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Completing the Square by Malin Christersson

Completing the Square by Malin Christersson
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2014-02-18 06:46
FunctionCoordinate GeometryGeometric Construction
This example demonstrates how to construct a complete square using the method of completing the square. Key mathematical concepts include quadratic terms, polynomials, and geometric construction. It uses commands like Polygon, Circle, OrthogonalLine, Point, Ray, and Intersect in GeoGebra. Suitable for middle and high school students learning quadratic equations and geometric construction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → largeSquare, a, b, c, d, stopR1, stopR2
  2. Circle(stopR1, B) → largeCircle
  3. OrthogonalLine(stopR2, a) → f
  4. OrthogonalLine(stopR2, f) → h
  5. OrthogonalLine(A, f) → g
  6. Point(g) → RayPoint
  7. Ray(B, RayPoint) → i
  8. Point(i) → C
  9. Circle(B, C) → smallCircle
  10. OrthogonalLine(C, g) → j
  11. Intersect(h, j) → D
  12. Circle(D, stopR1) → k
  13. Intersect(k, h, 2) → E
  14. Semicircle(stopR1, E) → p
  15. Point(p) → R1
  16. Line(D, R1) → m
  17. OrthogonalLine(R1, m) → n
  18. Circle(R1, Radius[largeCircle]) → r
  19. Intersect(r, n, 1) → H
  20. Circle(H, Radius[smallCircle]) → s
  21. Intersect(s, n) → G, J
  22. Semicircle(G, J) → q_1
  23. OrthogonalLine(H, n) → q
  24. Intersect(q_1, q) → K,
  25. OrthogonalLine(stopR1, a) → e
  26. OrthogonalLine(E, h) → l
  27. Intersect(l, i) → F
  28. Distance(A, B) → xLength
  29. Distance(B, C) → halfb_1
  30. Intersect(s, q, 2) → I
  31. Polygon(B, C, D, stopR1) → poly3, b_1, c_1, d_2, stopr1
  32. Intersect(largeCircle, e, 2) → startR2
  33. CircleArc(stopR1, startR2, stopR2) → t
  34. Point(t) → R2
  35. Line(stopR1, R2) → a_1
  36. Circle(stopR1, Radius[smallCircle]) → e_1
  37. Circle(R2, Radius[smallCircle]) → f_1
  38. OrthogonalLine(R2, a_1) → j_1
  39. OrthogonalLine(stopR1, a_1) → k_1
  40. Intersect(e_1, k_1, 1) → L
  41. Intersect(f_1, j_1, 1) → M
  42. Polygon(R2, stopR1, L, M) → rect2, k_2, stopr1_1, l_1, m_1
  43. Semicircle(stopR1, E) → p_1
  44. Intersect(p_1, j, 1) → N
  45. Polygon(stopR1, D, N, L) → smallSquare, stopr1_2, d_3, n_1, l_2
  46. Intersect(r, m) → O, P
  47. Semicircle(P, O) → r_1
  48. Intersect(r_1, n) → Q,
  49. Circle(Q, Radius[smallCircle]) → s_1
  50. OrthogonalLine(Q, n) → t_1
  51. Intersect(s_1, n) → R, S
  52. Semicircle(R, S) → c_2
  53. Intersect(c_2, t_1) → T,
  54. Polygon(D, T, Q, R1) → rect1, d_1, t_2, q_2, r1