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Completing the Square Demo

Completing the Square Demo
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2017-05-31 06:31
FunctionCoordinate GeometryCalculusParametric Equation
This example demonstrates the transformation of a quadratic function into vertex form using the completing the square method, visually showing the changes in the vertex of the parabola. It involves core mathematical concepts such as quadratic functions, completing the square, vertex coordinates, and analytical geometry. Key construction elements include RandomElement for parameter generation, and commands like Circle, Polygon, Line, Point, Segment, along with objects like PointIn, Intersect, and Textfield for interactive visualization. Suitable for high school mathematics teaching to help students understand the method and its applications.

GeoGebra Commands & Parameters

  1. RandomElement({1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}) → n
  2. RandomElement({1, 2, 3, 4, 5}) → a
  3. Circle(B, n) → p
  4. Polygon(A, B, 4) → poly1, b, c, d, e, C, D
  5. Line(C, B) → k
  6. Point(Circle[A, abs(n)]) → F
  7. Segment(A, F) → g
  8. Point(Circle[A, abs(n)]) → G
  9. Segment(A, G) → h
  10. Point(Circle[D, abs(n)]) → H
  11. Segment(D, H) → i
  12. Polygon(A, D, H, G) → poly3, a_2, d_1, h_1, g_1
  13. Point(Circle[G, abs(n)]) → I
  14. Segment(G, I) → j
  15. Polygon(F, I, G, A) → poly4, f_2, i_1, g_2, a_3
  16. PointIn(poly1) → Pointpoly1_1
  17. PointIn(poly3) → Pointpoly3_1
  18. PointIn(poly4) → Pointpoly4
  19. PointIn(poly1) → Pointpoly1
  20. Intersect(p, k) → E, J
  21. Polygon(B, E, F, A) → poly2, b_1, e_1, f, a_1
  22. PointIn(poly2) → Pointpoly2_1
  23. PointIn(poly2) → Pointpoly2
  24. PointIn(poly3) → Pointpoly3
  25. Textfield(t) → inputBox1
  26. Polygon(B, J, F, A) → poly5, b_2, j_1, f_1, a_4
  27. PointIn(poly5) → Pointpoly5