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Quadratic Formula Visualization

Quadratic Formula Visualization
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2018-01-11 08:53
FunctionCoordinate GeometryDerivativeOptimizationGraphing
This example dynamically demonstrates the quadratic formula, visually linking roots to coefficients. Core concepts include quadratic equations, the quadratic formula, discriminant, and function graphing. GeoGebra commands like If, Intersect, Point, and Vector are used to construct root loci, discriminant sign changes, and function graphs. Ideal for high school mathematics education to understand quadratic properties and geometric interpretations of the formula.

GeoGebra Commands & Parameters

  1. If(c < 0, "-", "+") → signcc
  2. If(c ≠ 0, signcc + absc, "") → text6
  3. If(b < 0, "-", "+") → signbb
  4. If(a < 0, "-", "") → signa
  5. If(a ≟ 0, "", If[absa ≟ 1, signa + "x^2", a + "x^2"]) → text5
  6. If(b ≟ 0, "", If[a ≠ 0 ∧ absb ≠ 1, signbb + absb + "x", signbb + "x"]) → text7
  7. If(b < 0, "-", "") → signb
  8. If(c < 0, "-", "") → signc
  9. If(a < 0, "-", "+") → signaa
  10. If(b < 0, "(" + b + ")", "" + b) → text3
  11. If(c < 0, "(" + c + ")", "" + c) → text4
  12. If(a < 0, "(" + a + ")", "" + a) → text11
  13. If(a < 0, "(" + a + ")", "" + a) → text11_1
  14. Intersect(d, xAxis) → A, B
  15. Point(e) → C
  16. Point(e) → D_1
  17. Vector(C, D_1) → u
  18. Point(f) → E
  19. Point(f) → F
  20. Vector(E, F) → v
  21. If(Disc ∈ list1, "", ("x=" * sol_3)) → text22
  22. If(Disc ∈ list1, "", "x=" + sol_4) → text23