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Completing the Square for Quadratic Equation (I)

Completing the Square for Quadratic Equation (I)
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2017-02-27 17:36
FunctionCoordinate GeometrySlider Animation
This example demonstrates the transformation of a quadratic equation into vertex form using the completing the square method, visually showing the changes in the parabola's vertex. Core mathematical concepts include quadratic equations, completing the square, vertex form, and parabolas. It utilizes commands like Point, Midpoint, RandomElement, Vector, Simplify, Intersect, Polygon, Dilate, and Translate to construct the graph dynamically, with sliders for parameter adjustment. Suitable for high school mathematics education to help students understand the application of the completing the square method and parabolic properties.

GeoGebra Commands & Parameters

  1. Point(yAxis) → D
  2. Point(xAxis) → B
  3. Midpoint(B, D) → M_{BD}
  4. RandomElement({-7, -6, -5, -4, -3, -2, -1, 7, 6, 5, 4, 3, 2, 1}) → a
  5. Vector(P_{xsquared}, M_{BD}) → u_1
  6. Random(-7, 7) → b
  7. Simplify((x - a)^(2) - c^(2)) → sl1
  8. Simplify(y^(2) + (b2 * y)) → sr2
  9. Simplify((-((x - a)^(2) - c^(2) - x^(2) - (a2 * x)))) → s3
  10. Simplify(x^(2) + (a2 * x)) → s4
  11. Simplify((x - a)^(2)) → sl5
  12. Simplify((y - b)^(2)) → sr5
  13. Simplify(x - h) → sl6
  14. Intersect(xAxis, yAxis) → A
  15. Polygon(A, B, C, D) → poly1, a_1, b_1, c_1, d_1
  16. Point(xAxis) → E
  17. Point(xAxis) → F
  18. Polygon(E, F, G, H) → poly2, e_1, f_1, g_1, h_1
  19. Polygon(I, J, K, L) → poly3, i_1, j_1, k_1, l_1
  20. Polygon(M, N, O, P) → poly4, m_1, n_1, o_1, p_1
  21. Dilate(M, h / a, O) → M'
  22. Dilate(N, h / a, O) → N'
  23. Dilate(O, h / a, O) → O'
  24. Dilate(P, h / a, O) → P'
  25. Polygon(M', N', O', P') → poly4', m', n', o', p'
  26. Midpoint(A, B) → M_{AB}
  27. Midpoint(A, D) → M_{AD}
  28. Midpoint(E, F) → M_{EF}
  29. Midpoint(F, H) → M_{FH}
  30. Midpoint(I, L) → M_{IL}
  31. Midpoint(J, L) → M_{JL}
  32. Midpoint(N', P') → M_{NP}
  33. Translate(P_{xsquared}, Vector[(n_{motion} * u_1)]) → R
  34. Vector(P_{xsquared}, R) → v_1
  35. Vector(P_{bx}, M_{FH}) → u_2
  36. Translate(P_{bx}, Vector[(n_{motion} * u_2)]) → Q
  37. Vector(P_{bx}, M_{JL}) → u_3
  38. Translate(P_{bx}, Vector[(n_{motion} * u_3)]) → S
  39. Vector(P_{bx}, Q) → v_2
  40. Vector(P_{bx}, S) → v_3
  41. Dilate(M, j / a^(2), O) → M'_1
  42. Dilate(N, j / a^(2), O) → N'_1
  43. Dilate(O, j / a^(2), O) → O'_1
  44. Dilate(P, j / a^(2), O) → P'_1
  45. Polygon(M'_1, N'_1, O'_1, P'_1) → poly4'_1, m'_1, n'_1, o'_1, p'_1
  46. Random((-(a2 / 2)^(2)) + 1, 8) → c_R