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Solving Quadratic Equations by Completing the Square by Sharon Mahon

Solving Quadratic Equations by Completing the Square by Sharon Mahon
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2019-07-16 02:38
FunctionCoordinate Geometry
This example demonstrates solving quadratic equations by completing the square. Key mathematical concepts include quadratic functions, completing the square, and equation solving. It uses commands like Segment, Polygon, Sequence, Point, etc., in GeoGebra. Suitable for middle school and above students to learn solving quadratic equations.

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
  37. Textfield(e) → InputBox2