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质心：二次函数

质心：二次函数
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2016-03-26 08:15
函数解析几何几何作图
本范例演示二次函数的质心。它涉及二次函数的核心数学概念，通过使用GeoGebra命令如IntegralBetween、Intersect等，展示了如何构造二次函数的质心。适合高中数学教学和学习二次函数性质。

GeoGebra 命令及参数

  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