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Quadratic Functions Practice Quiz: Solve, Vertex, Discriminant

Quadratic Functions Practice Quiz: Solve, Vertex, Discriminant
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2020-11-12 17:53
FunctionOptimizationInequalityGraphing
This interactive GeoGebra example is a practice quiz on quadratic functions, demonstrating how to solve quadratic equations, find the vertex, and use the discriminant to determine the nature of roots. Core math concepts include the standard form of a quadratic function, solving by factoring or quadratic formula, vertex formula, discriminant (Δ=b²-4ac), and relationships between coefficients and roots. Construction highlights: uses Textfield and InputBox for user input, Random and RandomElement to generate random coefficients, and commands like If, Extremum, Simplify, Coefficients, Element, AreEqual, and Factor to compute and verify answers. Suitable for middle school (upper grades) to high school students for classroom practice or self-study, providing immediate feedback on quadratic function skills.

GeoGebra Commands & Parameters

  1. Textfield(q3styvt) → InputBox4
  2. Random(1, 3) → q3ran
  3. Random(1, 8) → kK
  4. RandomElement(r1list) → r1
  5. Remove(r1list, {r1}) → r2list
  6. RandomElement(r2list) → r2
  7. RandomElement(alist) → aA
  8. Expand((aA * (x - r1)^(2)) + kK) → f4
  9. Expand((-f4(x))) → g4
  10. If(aA ≟ 1, ((x - r1) * (x - r2)), ((aA * (x - r1)) * (x - r2))) → f1
  11. If(q3ran ≟ 1, f1, If[q3ran ≟ 2, f4, g4]) → q3f
  12. Extremum(q3f) → Q3VTX
  13. Textfield(q3stxv) → InputBox3
  14. Textfield(q2stx1) → InputBox1
  15. Random(1, 3) → q2ran
  16. Random(-20, -1) → extrac
  17. Expand(f1) → f2
  18. Simplify(f2(x) + extrac) → f3
  19. Expand((-f3(x))) → g3
  20. If(q2ran ≟ 1, f2, If[q2ran ≟ 2, f3, g3]) → q2f
  21. Coefficients(q2f) → q2coeflist
  22. Element(q2coeflist, 3) → q2cC
  23. Element(q2coeflist, 2) → q2bB
  24. Element(q2coeflist, 1) → q2aA
  25. Textfield(q2stx2) → InputBox2
  26. Expand((aA * (x - r1)^(2))) → f5
  27. Random(1, 6) → q1ran
  28. If(q1ran ≟ 1, f2, If[q1ran ≟ 2, f3, If[q1ran ≟ 3, g3, If[q1ran ≟ 4, f4, If[q1ran ≟ 5, g4, f5]]]]) → q1f
  29. SelectedElement(q1droplist) → stansq1
  30. AreEqual(InputBox3, q3ansx) → corrq3a
  31. AreEqual(InputBox4, q3ansy) → corrq3b
  32. If(q1ran ≟ 6, 1, If[q1ran ≟ 4 ∨ q1ran ≟ 5, 0, 2]) → ansq1
  33. Coefficients(q1f) → q1coefflist
  34. Element(q1coefflist, 1) → q1aA
  35. Element(q1coefflist, 2) → q1bB
  36. Element(q1coefflist, 3) → q1cC
  37. If(ansq1 ≟ 0, "<0", If[ansq1 ≟ 1, "=0", ">0"]) → solq1txta
  38. If(aA ≟ 1, "", Text[aA]) → aAtxtif
  39. Coefficients(q3f) → q3coefflist
  40. Element(q3coefflist, 1) → q3aA
  41. Element(q3coefflist, 2) → q3bB
  42. Element(q3coefflist, 3) → q3cC
  43. Factor(q2f) → q2fsol

AI Drawing Prompt Reference

Create an interactive graph demonstrating how to solve quadratic equations, find the vertex, and use the discriminant to determine the nature of roots for quadratic functions. Include the graph of a quadratic function in standard form, solutions by factoring or quadratic formula, vertex formula, discriminant (Δ=b²-4ac), and the relationship between coefficients and roots. Allow users to input coefficients, generate random quadratic functions, display the vertex, and show the results of the discriminant for classroom practice or self-study.
The prompt above was compiled from the original drawing commands and is for reference only.