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Sketching Compressions of Parabolas

Sketching Compressions of Parabolas
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2018-12-06 23:13
FunctionCoordinate GeometryOptimizationGraphing
This example demonstrates how to sketch and analyze compressions of parabolas using GeoGebra. It involves core math concepts like parabolas, quadratic equations, optimization problems, and linear equations. Key GeoGebra commands and objects used in the construction include Polygon, PointIn, Element, LaTeX, and FitPoly. Suitable for high school and above students to understand function transformations and optimization problems.

GeoGebra Commands & Parameters

  1. Polygon({(-5.25, -5.25), (-5.25, 5.25), (5.25, 5.25), (5.5, -5.25)}) → viewBox
  2. PointIn(viewBox) → C
  3. PointIn(viewBox) → A
  4. PointIn(viewBox) → B
  5. PointIn(viewBox) → E
  6. PointIn(viewBox) → D
  7. Element(questionList, questionListIndex) → questionNum
  8. LaTeX(UnicodeToLetter[10007]) → xmark
  9. LaTeX(UnicodeToLetter[10003]) → cmark
  10. Element(P2:P11, questionNum) → correctPoints
  11. Element(D2:D11, questionNum) → functionText
  12. LaTeX((("\vphantom{\left(\tfrac{1}{2}\right)}" * functionText) * "")) → displayEquation
  13. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  14. FitPoly(startingPoints, 2) → fPoly
  15. FitPoly(correctPoints, 2) → gPolyDotted
  16. FitPoly(usersPoints, 2) → gPolySolid
  17. Element(A2:A11, questionNum) → a
  18. Element(B2:B11, questionNum) → h
  19. Element(C2:C11, questionNum) → k

AI Drawing Prompt Reference

To draw a graph of compressed parabolas. First, create a rectangle as the viewBox. Then, place points A, B, C, D, E. Next, add text elements like xmark, cmark, displayEquation, and TEXT. Finally, use FitPoly to fit parabolas, generating fPoly, gPolyDotted, and gPolySolid.
The prompt above was compiled from the original drawing commands and is for reference only.