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Practice Sketching Quadratic Functions in Vertex Form

Practice Sketching Quadratic Functions in Vertex Form
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2017-06-22 13:49
FunctionCoordinate GeometryGraphing
This practice contains 14 questions on sketching quadratic curves given the vertex or completed square form. Key math concepts include quadratic functions, coordinate geometry, and geometric construction. GeoGebra commands used include Shuffle, Sequence, If, Random, etc. Suitable for middle school and above students for self-assessment and practice.

GeoGebra Commands & Parameters

  1. Shuffle({9, 11, 13, 15}) → listshowGf1, {9, 11, 15, 13}
  2. Shuffle({10, 12, 14, 16}) → listshowGf2, {10, 16, 12, 14}
  3. Shuffle({9, 10, 13, 14}) → listshowGf3, {9, 14, 13, 10}
  4. Shuffle({11, 12, 15, 16}) → listshowGf4, {16, 11, 15, 12}
  5. Shuffle({9, 12, 13, 16}) → listshowGf5, {13, 16, 9, 12}
  6. Shuffle({10, 11, 14, 15}) → listshowGf6, {15, 10, 11, 14}
  7. Sequence(If[count < 3, Element[listshowGf0, i], If[count < 5, Element[listshowGf1, i], If[count < 7, Element[listshowGf2, i], If[count < 9, Element[listshowGf3, i], If[count < 11, Element[listshowGf4, i], If[count < 11, Element[listshowGf5, i], Element[listshowGf6, i]]]]]]], i, 1, 4) → listnsG
  8. If(useG, If[count > 2, Random[0, 7], 3], Random[0, 7]) → e'
  9. Random(1, 4) → d
  10. If(count > 2, Random[1, 4], If[count > 1, 3, 1]) → n_g
  11. If(d ≟ e' ∧ (count > 8 ∨ count < 5), 1, e') → e
  12. Random(1, 4) → n_f
  13. Shuffle({1, 2, 3, 4}) → listshowFf1, {3, 1, 4, 2}
  14. Shuffle({1, 4, 5, 8}) → listshowFf2a, {1, 5, 4, 8}
  15. Shuffle({2, 3, 6, 7}) → listshowFf2b, {6, 3, 7, 2}
  16. If(count < 5, Element[listFf, Element[listshowFf1, 3]], If[count < 9, Element[listFf, Element[listshowFf2a, 3]], Element[listFf, Element[listshowFf2b, 3]]]) → f_{3s}
  17. Coefficients(f_{3s}) → listf_{3s}
  18. If(count < 5, Element[listFf, Element[listshowFf1, 4]], If[count < 9, Element[listFf, Element[listshowFf2a, 4]], Element[listFf, Element[listshowFf2b, 4]]]) → f_{4s}
  19. Coefficients(f_{4s}) → listf_{4s}
  20. If(count < 5, Element[listFf, Element[listshowFf1, 1]], If[count < 9, Element[listFf, Element[listshowFf2a, 1]], Element[listFf, Element[listshowFf2b, 1]]]) → f_{1s}
  21. Coefficients(f_{1s}) → listf_{1s}
  22. If(count < 5, Element[listFf, Element[listshowFf1, 2]], If[count < 9, Element[listFf, Element[listshowFf2a, 2]], Element[listFf, Element[listshowFf2b, 2]]]) → f_{2s}
  23. Coefficients(f_{2s}) → listf_{2s}
  24. Element(listCoeffs, n_f, 1) → a_f
  25. Element(listCoeffs, n_f, 2) → b_f
  26. Sequence(Sequence[(x(A) + (s_p * i), y(A) + (s_p * j)), i, 0, 3], j, 0, 0) → list3CtrofGraphs, {{(5, 0), (13.8, 0), (22.6, 0), (31.400000000000002, 0)}}
  27. Polygon(E, D, F, G) → poly2, e_1, d_1, f_5, g
  28. Polygon(J, K, L, M) → poly4, j, k, l, m
  29. Polygon(J, K, C, B) → poly5, j_1, k_1, c, b_1
  30. Sequence(Sequence[Segment[(x(A) + (s_p * i) - l_x / 2, y(A) + (s_p * j)), (x(A) + (s_p * i) + l_x / 2, y(A) + (s_p * j))], i, 0, 3], j, 0, 0) → list1Xaxes, {{7.6000000000000005, 7.600000000000001, 7.600000000000001, 7.600000000000001}}
  31. Sequence(Sequence[Segment[(x(A) + (s_p * i), y(A) + (s_p * j) - l_y / 2), (x(A) + (s_p * i), y(A) + (s_p * j) + l_y / 2)], i, 0, 3], j, 0, 0) → list2Yaxes, {{10, 10, 10, 10}}
  32. Sequence(Sequence[(x(A) + l_x / 2 + (s_p * i), y(A) + (s_p * j)), i, 0, 3], j, 0, 0) → listXarrow, {{(8.8, 0), (17.6, 0), (26.400000000000002, 0), (35.2, 0)}}
  33. Sequence(Sequence[(x(A) + (s_p * i), y(A) + l_y / 2 + (s_p * j)), i, 0, 3], j, 0, 0) → listYarrow, {{(5, 5), (13.8, 5), (22.6, 5), (31.400000000000002, 5)}}
  34. Sequence(Sequence[Text[Element[listChoicestext, i + 1], (x(A) - l_x / 2 + (s_p * (i - 1)), y(A) + l_y / 2)], i, 1, 4], j, 0, 0) → listChoicestextDisplay, {{"(a)", "(b)", "(c)", "(d)"}}
  35. Element(listCoeffs, n_f, 3) → c_f
  36. If(useG, x(Element[listTurningPointsG, Element[listnsG, n_g] - 8]), ((-b_f)) / ((2 * a_f))) → symx2
  37. Defined(root1) → realroots
  38. If(count < 5, Element[listFf, Element[listshowFf1, 4]], If[count < 9, Element[listFf, Element[listshowFf2a, 4]], Element[listFf, Element[listshowFf2b, 4]]]) → f_{tests}
  39. Polygon(B, C, D, E) → poly1, b, c_1, d_2, e_2
  40. If(count < 5, Element[listshowFf1, n_f], If[count < 9, Element[listshowFf2a, n_f], Element[listshowFf2b, n_f]]) → n_s
  41. Sequence(If[count < 5, Element[listshowFf1, i], If[count < 9, Element[listshowFf2a, i], Element[listshowFf2b, i]]], i, 1, 4) → listnsF
  42. Sequence({Cell[9, Element[listnsF, i]], Cell[10, Element[listnsF, i]]}, i, 1, 4) → listfsroots
  43. Min(d, e) → I1
  44. Min((-d), e) → I2
  45. Min(d, (-e)) → I3
  46. Min((-d), (-e)) → I4
  47. Min(d, e) → I5
  48. Min((-d), e) → I6
  49. Min(d, (-e)) → I7
  50. Min((-d), (-e)) → I8
  51. Max(d, e) → J1
  52. Max((-d), e) → J2
  53. Max((-d), e) → J6
  54. Max(d, (-e)) → J7
  55. Max(d, (-e)) → J3
  56. Max((-d), (-e)) → J4
  57. Max(d, e) → J5
  58. Max((-d), (-e)) → J8
  59. If(e ≟ 0, Element[listGf, Element[listshowGf0, 1] - 8], Element[listGf, Element[listnsG, 1] - 8]) → g_{1s}
  60. If(e ≟ 0, Element[listGf, Element[listshowGf0, 2] - 8], Element[listGf, Element[listnsG, 2] - 8]) → g_{2s}
  61. If(e ≟ 0, Element[listGf, Element[listshowGf0, 4] - 8], Element[listGf, Element[listnsG, 4] - 8]) → g_{4s}
  62. If(e ≟ 0, Element[listGf, Element[listshowGf0, 3] - 8], Element[listGf, Element[listnsG, 3] - 8]) → g_{3s}
  63. Sequence((0, Cell[7, 8 + i]), i, 1, 8) → listyintercepts
  64. Element(Coefficients[Simplify[Cell[6, Element[listnsG, n_g]]]], 2) → b_g
  65. Element(Coefficients[Simplify[Cell[6, Element[listnsG, n_g]]]], 3) → c_g
  66. Element(Coefficients[Simplify[Cell[6, Element[listnsG, n_g]]]], 1) → a_g
  67. Textfield(textname) → InputBoxName
  68. Textfield(classname) → InputBox1