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Visualizing Quadratic Functions ax²+bx+c=0

Visualizing Quadratic Functions ax²+bx+c=0
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2020-03-01 04:29
FunctionCoordinate GeometryCalculusOptimizationGraphing
This example visually demonstrates the graph and properties of quadratic functions ax²+bx+c=0. It covers core math concepts like parabola, function graph, vertex, axis of symmetry, and intersection points. Key GeoGebra commands used include Intersect, Extremum, Function, Segment, Point, Polygon, and If. Suitable for high school students learning quadratic function graphs, properties, and geometric transformations.

GeoGebra Commands & Parameters

  1. Intersect(f, xAxis) → A, B
  2. Extremum(f) → S
  3. Function(f, -8, 8) → h
  4. Segment(J, K) → e
  5. Segment(L, M) → g
  6. Segment(N, O) → i
  7. Segment(O, P) → j
  8. Segment(P, Q) → k
  9. Segment(R, S_1) → l
  10. Segment(S_1, T) → m
  11. Segment(T, U) → n
  12. Segment(V, W) → p
  13. Segment(Z, A1) → q
  14. Point(xAxis) → C
  15. Point(xAxis) → B1
  16. Point(xAxis) → C1
  17. Point(xAxis) → D1
  18. Point(xAxis) → E1
  19. Point(xAxis) → F1
  20. Point(xAxis) → G1
  21. Point(xAxis) → H1
  22. Intersect(xAxis, yAxis) → I1
  23. Point(xAxis) → J1
  24. Point(xAxis) → K1
  25. Point(xAxis) → L1
  26. Point(xAxis) → M1
  27. Point(xAxis) → N1
  28. Point(yAxis) → P1
  29. Point(yAxis) → Q1
  30. Point(yAxis) → R1
  31. Point(yAxis) → S1
  32. Point(yAxis) → T1
  33. Point(yAxis) → U1
  34. Point(yAxis) → V1
  35. Point(yAxis) → W1
  36. Point(yAxis) → Z1
  37. Point(yAxis) → A2
  38. Point(yAxis) → C2
  39. Point(yAxis) → D2
  40. Point(yAxis) → E2
  41. Point(yAxis) → G2
  42. Point(yAxis) → H2
  43. Point(yAxis) → I2
  44. Point(yAxis) → J2
  45. Point(yAxis) → K2
  46. Point(yAxis) → L2
  47. Point(yAxis) → M2
  48. Point(yAxis) → N2
  49. Point(yAxis) → O2
  50. Point(yAxis) → F2
  51. Point(yAxis) → B2
  52. Point(yAxis) → P2
  53. Point(yAxis) → Q2
  54. Point(yAxis) → R2
  55. Point(yAxis) → S2
  56. Point(yAxis) → U2
  57. Point(yAxis) → V2
  58. Point(yAxis) → W2
  59. Point(yAxis) → Z2
  60. Point(xAxis) → A3
  61. Point(xAxis) → B3
  62. Point(xAxis) → C3
  63. Point(xAxis) → D3
  64. Point(xAxis) → E3
  65. Point(xAxis) → F3
  66. Point(xAxis) → G3
  67. Point(xAxis) → H3
  68. Point(xAxis) → I3
  69. Point(xAxis) → J3
  70. Point(xAxis) → K3
  71. Point(xAxis) → L3
  72. Point(xAxis) → M3
  73. Point(xAxis) → O1
  74. Point(xAxis) → N3
  75. Point(xAxis) → O3
  76. Point(xAxis) → P3
  77. Point(yAxis) → Q3
  78. Point(xAxis) → R3
  79. Point(yAxis) → S3
  80. Segment(H5, I5) → d
  81. Polygon(J5, K5, L5, M5) → poly1, j5_1, k5_1, l5_1, m5_1
  82. Polygon(A_1, B_1, C_1, D_1) → poly2, a_1, b_1, c_1, d_1
  83. Polygon(A_1, D_1, C_1, B_1) → poly3, a_2, d_2, c_2, b_2
  84. If(X1 > 0, "", "+") → plus1
  85. If(X2 > 0, "", "+") → plus2
  86. If(seul < 0, "+", "") → plus3

AI Drawing Prompt Reference

Draw a quadratic function parabola in standard form. First plot the curve itself, then mark its two intersection points with the x-axis and its vertex (extremum). Place multiple points along the x-axis and y-axis to serve as grid references. From these axis points, draw several vertical and horizontal segments to form an auxiliary grid or framework around the parabola. Also mark the origin where the axes intersect. The overall image shows a parabola with grid lines, highlighting its shape, axis of symmetry, and key intersection points.
The prompt above was compiled from the original drawing commands and is for reference only.