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Completing the Square - Novice

Completing the Square - Novice
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2017-04-07 19:44
FunctionCoordinate GeometryOptimization
This example demonstrates the application of completing the square in quadratic functions through dynamic geometry, visually presenting vertex transformation. Core math concepts include quadratic functions, completing the square, vertex coordinates, and function graph transformations. Construction highlights derived from GeoGebra commands: Polygon, Distance, Perimeter, PointIn, Textfield. Suitable for middle school students and above to learn the properties of quadratic functions and the geometric meaning of completing the square, or for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Polygon(A, D, G, C) → poly1, a_1, d_1, g_1, c_1
  2. Polygon(A, E, F, B) → poly2, a_2, e, f_1, b_3
  3. Polygon(A, E, H, C) → poly3, a_3, e_1, h, c_2
  4. Polygon(H, G, I, F) → poly4, h_1, g_2, i, f_2
  5. Distance(A, C) → distanceAC
  6. Distance(A, E) → distanceAE
  7. Distance(A, H) → distanceAH
  8. Distance(E, D) → distanceED
  9. Distance(C, B) → distanceCB
  10. Distance(E, G) → distanceEG
  11. Distance(C, F) → distanceCF
  12. Distance(H, I) → distanceHI
  13. Polygon(A, J, K, L) → poly5, a_4, j_1, k, l
  14. Polygon(J, M, N, K) → poly6, j_2, m, n, k_1
  15. Polygon(J, M, N, K) → poly8, j_3, m_1, n_1, k_3
  16. Polygon(K, P, O, L) → poly7, k_2, p, o, l_1
  17. Polygon(K, P, O, L) → poly9, k_4, p_1, o_1, l_2
  18. Polygon(R, T, Q, S) → poly10, r_9, t, q_1, s
  19. Polygon(R, T, Q, S) → poly11, r_{10}, t_1, q_2, s_1
  20. Distance(A, U) → distanceAU
  21. Distance(A, V) → distanceAV
  22. Distance(A, R) → distanceAR
  23. Polygon(R, T, Q, S) → poly12, r_{11}, t_2, q_3, s_2
  24. Distance(R, Q) → distanceRQ
  25. Perimeter(poly12) → perimeterpoly12
  26. PointIn(poly12) → Pointpoly12
  27. Textfield(g_{10}) → InputBox1
  28. Textfield(g_{11}) → InputBox2