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Graphing Quadratic Equations II (Self Assessment)

Graphing Quadratic Equations II (Self Assessment)
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2017-02-17 14:33
FunctionGraphing
This example demonstrates how to solve quadratic equations with algebraic expressions on both sides using graphical methods. It requires an additional step to rearrange the equation into standard form before plotting the function graphs to find intersection points, thereby determining the roots. Key math concepts include quadratic functions, function graphs, and intersection solving. GeoGebra commands and objects used in construction are Sequence, Union, Simplify, Root, Textfield, Roots, Extremum, If, Point, Intersect, suitable for high school students to understand the relationship between function graphs and equation solutions, enhancing self-assessment skills.

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. Sequence(i, i, -13, 13, 1) → list3
  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, -30, 30) → 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(abs(x(C) - Min[userx1, userx2]) < 0.055, true, false) → correctxmin
  19. If(abs(x(D) - Max[userx1, userx2]) < 0.055, true, false) → correctxmax
  20. If(b^(2) < (4 * ac), nosolncorrect, correctxmax ∧ correctxmin) → correctroots
  21. Point(f) → P
  22. Simplify((-c)) → c_2
  23. Simplify((a * x^(2)) + (b * x)) → f_2
  24. Simplify((a * x^(2))) → f_3
  25. Simplify(((-b) * x) - c) → bc_3
  26. Textfield(inputf) → InputBox6
  27. If(f_{userinput} ≟ f, true, false) → correctfunction
  28. If(correctfunction ∧ correctroots ∧ checkedroots ∨ checkrootcounter > 1, true, false) → showbutton1
  29. If(correctfunction ∧ correctroots ∨ checkrootcounter > 1, true, false) → n
  30. If(correctfunction ∧ correctroots ∨ checkrootcounter > 1, true, false) → o
  31. If(correctfunction ∧ correctroots ∨ checkrootcounter > 1, true, false) → p
  32. If(correctfunction ∧ correctroots ∨ checkrootcounter > 1, true, false) → q
  33. If(correctfunction ∧ correctroots ∨ checkrootcounter > 1, true, false) → r
  34. If(correctfunction ∧ correctroots ∨ checkrootcounter > 1, true, false) → s
  35. If(correctfunction ∧ correctroots ∨ checkrootcounter > 1, true, false) → t
  36. If(correctfunction ∧ correctroots ∨ checkrootcounter > 1, true, false) → u
  37. If(correctfunction ∧ correctroots ∨ checkrootcounter > 1, true, false) → v
  38. If(correctfunction ∧ correctroots ∨ checkrootcounter > 1, true, false) → w
  39. If(y(E) < 0, y(E) + Min[(-abs((0.25 * y(E)))), -5], Min[-5, (-abs((0.25 * y(E))))]) → yMinView2
  40. If(y(E) > 0, y(E) + Max[(0.25 * y(E)), 5], Max[abs((0.25 * y(E))), 5]) → yMaxView2
  41. Intersect(f, xAxis) → F, G
  42. 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
  43. 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