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配方法解二次方程

配方法解二次方程
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2019-07-16 02:38
函数解析几何
本范例演示了配方法解二次方程的过程。核心数学概念包括二次函数、配方法和方程求解。使用了Segment, Polygon, Sequence, Point等GeoGebra命令。适合初中及以上学生学习二次方程的解法。

GeoGebra 命令及参数

  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
  37. Textfield(e) → InputBox2