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Graphing and Properties of x^2 - x Function

Graphing and Properties of x^2 - x Function
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2017-07-15 12:20
FunctionCalculusOptimizationGraphing
This example demonstrates the graph of the function x^2 - x and its key properties such as vertex, axis of symmetry, and zeros using GeoGebra. Core math concepts include quadratic functions, derivatives, integrals, symmetry, and function zeros. Construction highlights involve using commands like Intersect for intersection points, Integral for area calculation, Textfield for displaying information, Point for marking special points, Polygon and Segment for drawing shapes, Angle for measuring angles, and Circle for drawing circles. Suitable for high school mathematics teaching, focusing on function graph analysis and property exploration.

GeoGebra Commands & Parameters

  1. Intersect(f, h, (1.3247179572097767, 1.7548776662103318)) → A
  2. Integral(f(x) - h(x), 0, 1.32) → a
  3. Intersect(g, h, (-1.0782324076626095, 1.1625851241606506)) → B
  4. Integral(g(x) - h(x), -1.32, 0) → b
  5. Textfield(t) → InputBox1
  6. Intersect(h, p, (-1.5345410449425416, 2.3548162186133474)) → C
  7. Integral(p(x) - h(x), -1.8, 0) → c
  8. Point(h) → D
  9. Point(h) → E
  10. Point(h) → F
  11. Point(h) → G
  12. Polygon(B, D, E, F, G, C) → poly1, b_1, d, e, f_1, g_1, c_1
  13. Segment(B, A) → i
  14. Segment(A, C) → j
  15. Segment(C, B) → k
  16. Angle(C, A, B) → α
  17. Point(Circle[H, 0.71]) → I
  18. Segment(H, I) → l
  19. Point(Circle[I, 0.29]) → J
  20. Segment(I, J) → m
  21. Point(Circle[I, 0.71]) → K
  22. Segment(I, K) → n
  23. Circle(H, 1) → q
  24. Point(Circle[J, 1]) → L
  25. Segment(J, L) → r
  26. Point(Circle[L, 1]) → M
  27. Segment(L, M) → s
  28. Segment(H, L) → h_1
  29. Segment(M, H) → i_1
  30. Segment(N, O) → j_1
  31. Point(Circle[P, 0.3]) → Q
  32. Segment(P, Q) → k_1