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Solving Quadratic Equations with Formula

Solving Quadratic Equations with Formula
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2017-02-09 15:24
FunctionCoordinate GeometryOptimization
This example demonstrates solving quadratic equations using the formula. Key mathematical concepts include the roots of a quadratic equation, discriminant, and the quadratic formula. Using GeoGebra commands like Sequence, Union, and Simplify, the roots of the quadratic equation are constructed. Suitable for middle school and above students to learn how to solve quadratic equations.

GeoGebra Commands & Parameters

  1. Sequence(i, i, -20, 20, 1) → list3
  2. Sequence(i, i, 1, 20, 1) → list4
  3. Sequence(i, i, -20, -1, 1) → list1
  4. Union(list1, list4) → list5
  5. Sequence(i, i, -13, 15, 1) → list2
  6. Simplify((a * x^(2)) + (b * x) + c) → f
  7. Root(f) → A, B
  8. Textfield(inputa) → InputBox1
  9. Textfield(inputb) → InputBox2
  10. Textfield(inputc) → InputBox3
  11. Textfield(inputx1) → InputBox4
  12. Textfield(inputx2) → InputBox5
  13. Roots(f, -100, 100) → C, D
  14. Extremum(f, -30, 30) → E
  15. If(usera ≟ a, true, false) → correcta
  16. If(userb ≟ b, true, false) → correctb
  17. If(userc ≟ c, true, false) → correctc
  18. If(y(E) < 0, y(E) + Min[(-abs((0.25 * y(E)))), -5], Min[-5, (-abs((0.25 * y(E))))]) → yMinView2
  19. If(y(E) > 0, y(E) + Max[(0.25 * y(E)), 5], Max[abs((0.25 * y(E))), 5]) → yMaxView2
  20. Intersect(f, xAxis) → F, G
  21. If(abs(x(C) - Min[userx1, userx2]) < 0.015, true, false) → correctxmin
  22. If(abs(x(D) - Max[userx1, userx2]) < 0.01, true, false) → correctxmax
  23. If(If[discriminant < 0, x(E) + 5, If[discriminant ≟ 0, x(E) + 5, x(G) + (0.5 * abs(x(G) - x(F)))]] < 0, 1, If[discriminant < 0, x(E) + 5, If[discriminant ≟ 0, x(E) + 5, x(G) + (0.5 * abs(x(G) - x(F)))]]) → xMaxView2
  24. If(If[discriminant < 0, x(E) - 5, If[discriminant ≟ 0, x(E) - 5, x(F) - (0.5 * abs(x(G) - x(F)))]] > 0, -1, If[discriminant < 0, x(E) - 5, If[discriminant ≟ 0, x(E) - 5, x(F) - (0.5 * abs(x(G) - x(F)))]]) → xMinView2
  25. Expand(((x + RandomElement[{-1, 1, -2, 2, -3, 3, -4, 4, -5, 5}]) * (x + RandomElement[{-1, 1, -2, 2, -3, 3, -4, 4, -5, 5}]))) → f_{l1}
  26. Text(("x = " * x(C))) → textrootC
  27. Text(("x = " * x(D))) → textrootD