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Completing the Square (2) – Interactive Practice with Feedback

Completing the Square (2) – Interactive Practice with Feedback
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2017-05-02 02:24
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This GeoGebra example demonstrates the process of completing the square for quadratic functions through an interactive quiz-style generator with immediate feedback. The core mathematical concepts include transforming a quadratic expression into vertex form, perfect square trinomials, and algebraic equivalence. The construction uses GeoGebra commands such as Segment, Polygon, Sequence, Point, Dilate, Rotate, Vector, Translate, Distance, and Textfield, along with objects like polygons, points, sliders, and text input fields. These elements allow users to manipulate coefficients and visually see how the geometric area model corresponds to the algebraic steps. It is suitable for middle and high school students learning algebra and quadratic functions, as well as for teachers to use in classroom demonstrations or as a formative assessment tool.

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