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Effect of Coefficient b in Quadratic Functions

Effect of Coefficient b in Quadratic Functions
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2015-10-20 01:21
FunctionCoordinate GeometrySlider AnimationGraphing
This interactive GeoGebra worksheet demonstrates the effect of the coefficient b in the quadratic function y = a x² + b x + c on the shape and position of the parabola. It shows how varying b shifts the parabola horizontally, moves the vertex, and changes the axis of symmetry. The construction uses the commands Intersect to find intersections with the axes, Segment to draw key line segments, and Sequence to generate a series of parabolas for different b values, with sliders for dynamic adjustment. Suitable for high school students studying quadratic functions and teachers preparing visual lessons on function transformations.

GeoGebra Commands & Parameters

  1. Intersect(f, m, 1) → G
  2. Intersect(f, l, 1) → H
  3. Intersect(f, j, 1) → I
  4. Intersect(f, i, 1) → J
  5. Intersect(f, g, 1) → K
  6. Intersect(f, e, 1) → L
  7. Intersect(f, d, 1) → M
  8. Intersect(t, d) → A
  9. Intersect(t, e) → B
  10. Intersect(t, g) → C
  11. Intersect(t, j) → D
  12. Intersect(t, l) → E
  13. Intersect(t, m) → F
  14. Segment(A, M) → n
  15. Segment(B, L) → p
  16. Segment(C, K) → q
  17. Segment((0, 0), J) → r
  18. Segment(D, I) → s
  19. Segment(F, G) → a_1
  20. Segment(E, H) → c_3
  21. Sequence((a, f(a)), a, -10, 10) → list1
  22. Sequence(x = w, w, -10, 10) → list2
  23. Intersect(t, q_1, 1) → N
  24. Intersect(t, p_1, 1) → O
  25. Intersect(t, n_1, 1) → P
  26. Intersect(t, m_1, 1) → Q
  27. Intersect(t, l_1, 1) → R
  28. Intersect(t, k_1, 1) → S
  29. Intersect(t, j_1, 1) → T
  30. Intersect(t, i_1, 1) → U
  31. Intersect(t, h_1, 1) → V
  32. Intersect(t, g_1) → W
  33. Intersect(t, f_1, 1) → Z
  34. Intersect(t, e_1, 1) → A_1
  35. Intersect(t, d_1, 1) → B_1
  36. Intersect(t, b_1, 1) → C_1
  37. Intersect(f, b_1, 1) → D_1
  38. Intersect(f, d_1, 1) → E_1
  39. Intersect(f, e_1, 1) → F_1
  40. Intersect(f, f_1, 1) → G_1
  41. Intersect(f, g_1, 1) → H_1
  42. Intersect(f, h_1, 1) → I_1
  43. Intersect(f, i_1, 1) → J_1
  44. Intersect(f, j_1, 1) → K_1
  45. Intersect(f, k_1, 1) → L_1
  46. Intersect(f, l_1, 1) → M_1
  47. Intersect(f, m_1, 1) → N_1
  48. Intersect(f, n_1, 1) → O_1
  49. Intersect(f, p_1, 1) → P_1
  50. Intersect(f, q_1, 1) → Q_1
  51. Segment(D_1, C_1) → r_1
  52. Segment(E_1, B_1) → s_1
  53. Segment(F_1, A_1) → t_1
  54. Segment(G_1, Z) → a_2
  55. Segment(H_1, W) → b_2
  56. Segment(V, I_1) → c_2
  57. Segment(U, J_1) → d_2
  58. Segment(K_1, T) → e_2
  59. Segment(L_1, S) → f_2
  60. Segment(M_1, R) → g_2
  61. Segment(Q, N_1) → h_2
  62. Segment(O_1, P) → i_2
  63. Segment(P_1, O) → j_2
  64. Segment(Q_1, N) → k_2