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Centers of Mass: Quadratic Functions

Centers of Mass: Quadratic Functions
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2016-03-26 08:15
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the centers of mass for quadratic functions. It involves key mathematical concepts of quadratic functions and uses GeoGebra commands such as IntegralBetween and Intersect to construct the centers of mass. Suitable for high school mathematics education and learning about quadratic function properties.

GeoGebra Commands & Parameters

  1. IntegralBetween(((x^(m_d) * x) * f(x)), ((x^(m_d) * x) * g(x)), 0, b) → d
  2. IntegralBetween(((x^(m_d) * 0.5) * f(x)^(2)), ((x^(m_d) * 0.5) * g(x)^(2)), 0, b) → e
  3. IntegralBetween((x^(m_d) * f(x)), (x^(m_d) * g(x)), 0, b) → c_1
  4. Intersect(h, i) → B
  5. IntegralBetween(f, g, 0, b) → b_1
  6. Intersect(j, i) → C
  7. Intersect(g, h, (2.2499999999999996, 0)) → D
  8. Segment(C, B) → l_1
  9. Segment(D, B) → m
  10. OrthogonalLine(B, xAxis) → p
  11. Point(f) → G
  12. Point(g) → H
  13. Segment(G, H) → r
  14. Segment(I, J) → s
  15. Point(Circle[(0, 0), 10]) → K
  16. Segment((0, 0), K) → t
  17. OrthogonalLine(B, xAxis) → a
  18. Intersect(a, t) → M
  19. Segment((18.146457989754047, 4.372679273369628), (18.346457989754047, 4.372679273369628)) → l
  20. Segment((12.166855905735655, 4.343893410421017), (12.366855905735656, 4.343893410421017)) → k
  21. Intersect(f, q, (3, 9)) → O
  22. Intersect(q, a_1) → P
  23. Segment(O, P) → d_1