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Quadratic Function Graph by David T

Quadratic Function Graph by David T
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2012-12-05 07:51
FunctionCoordinate GeometryCalculusDerivativeGraphing
This example demonstrates the graphing of quadratic functions and their transformations. Key math concepts include quadratic functions, function graphs, axes of symmetry, vertex, and direction of opening. GeoGebra commands and objects like If, Expand, Intersect, Point, and GCD are used in the construction. Suitable for high school students learning function graphing and transformations, or introductory calculus education.

GeoGebra Commands & Parameters

  1. If(b < 1, "-", "") → signb
  2. If(a < 1, "-", "+") → signaa
  3. If(b < 1, "-", "+") → signbb
  4. If(a < 1, "-", "") → signa
  5. Expand(F_1 / F_2 * (x + a) * (x + b)) → expand
  6. If(a ≟ 0, "", "(") → LBr_a
  7. If(a ≟ 0, "", ")") → RBr_a
  8. If(b ≟ 0, "", "(") → LBr_b
  9. If(b ≟ 0, "", ")") → RBr_b
  10. Intersect(k, xAxis) → A, B
  11. Intersect(k, s) → D,
  12. Point(n) → C
  13. Intersect(k, n) → E,
  14. Intersect(k, yAxis) → F,
  15. If(a ≟ 0, "", signaa) → signaaa
  16. If(b ≟ 0, "", signbb) → signbbb
  17. If(absa ≟ 0, "", "" + absa) → absaa
  18. If(absb ≟ 0, "", "" + absb) → absbb
  19. If(Fact < 0, "-", "") → signFact
  20. GCD(F_1, F_2) → HCF
  21. If((a > 0) ∧ (b > 0) ∧ (HCF < 2) ∧ (den ≠ 1), "", If[den ≟ 0, " undefined", If[den ≠ 1, "\large{" + signFact + "} " + "\large \frac{" + num + "}{" + den + "}", signFact + num]]) → Fract

AI Drawing Prompt Reference

Draw the graph of a quadratic function, showing its transformations. Include the axis of symmetry, vertex, and direction of opening. First, plot the graphs of two functions, then mark their intersection points, vertex, and points where they intersect the coordinate axes. Use different colors and styles to distinguish the functions, and label the coordinates of key points. Finally, express the functions in formula form and show their factored and fractional forms.
The prompt above was compiled from the original drawing commands and is for reference only.