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Graphing to Solve Quadratic Equations I

Graphing to Solve Quadratic Equations I
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2017-02-16 17:49
FunctionOptimization
This example uses graphing to solve quadratic equations. It demonstrates the relationship between the graph of a quadratic function and its roots, involving key concepts such as roots and extrema. It utilizes commands like Sequence, Union, and RandomElement in GeoGebra, suitable for self-assessment and learning by middle school and above students.

GeoGebra Commands & Parameters

  1. Sequence(i, i, 1, 20, 1) → list4
  2. Sequence(i, i, -20, -1, 1) → list1
  3. Union(list1, list4) → list5
  4. Sequence(i, i, -7, 9, 1) → list2
  5. RandomElement(list2) → b
  6. Sequence(i, i, -13, 13, 1) → list3
  7. RandomElement(list3) → c
  8. Simplify((a * x^(2)) + (b * x) + c) → f
  9. Root(f) → A, B
  10. Textfield(inputa) → InputBox1
  11. Textfield(inputb) → InputBox2
  12. Textfield(inputc) → InputBox3
  13. Textfield(inputx1) → InputBox4
  14. Textfield(inputx2) → InputBox5
  15. Roots(f, -30, 30) → C, D,
  16. Extremum(f, -30, 30) → E
  17. If(discriminant < 0, x(E) - 5, If[discriminant ≟ 0, x(E) - 5, x(C) - abs(x(D) - x(C))]) → xMinView2
  18. If(y(E) < 0, y(E) + (0.2 * y(E)), (-abs((0.15 * y(E))))) → yMinView2
  19. If(y(E) > 0, y(E) + (0.2 * y(E)), abs((0.15 * y(E)))) → yMaxView2
  20. If(usera ≟ a, true, false) → correcta
  21. If(userb ≟ b, true, false) → correctb
  22. If(userc ≟ c, true, false) → correctc
  23. If(abs(x(C) - Min[userx1, userx2]) < 0.055, true, false) → correctxmin
  24. If(abs(x(D) - Max[userx1, userx2]) < 0.055, true, false) → correctxmax
  25. If(b^(2) < (4 * ac), nosolncorrect, correctxmax ∧ correctxmin) → correctroots
  26. Point(xAxis) → P
  27. If(If[discriminant < 0, x(E) + 5, If[discriminant ≟ 0, x(E) + 5, x(D) + abs(x(D) - x(C))]] < 0, 1, If[discriminant < 0, x(E) + 5, If[discriminant ≟ 0, x(E) + 5, x(D) + abs(x(D) - x(C))]]) → xMaxView2