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Identify Transformations

Identify Transformations
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2018-11-13 22:29
FunctionCoordinate GeometryCalculusTransformationGeometric Construction
This example demonstrates how to identify transformations of quadratic functions. Key mathematical concepts include transformations of quadratic equations. Using GeoGebra commands such as Random, RandomElement, and Shuffle, the transformation process is dynamically displayed. Suitable for high school math education, helping students understand horizontal and vertical translations, stretches, compressions, and reflections of quadratic functions.

GeoGebra Commands & Parameters

  1. Random(1, 9) → hTemp
  2. RandomElement({hTemp, (-hTemp)}) → h
  3. Shuffle({1, 2, 4, 5}) → factorList
  4. RandomElement({1, 2, 3, 4}) → aFactor
  5. Random(1, 9) → kTemp
  6. RandomElement({kTemp, (-kTemp)}) → k
  7. RandomElement({aFactor, (-aFactor), 1 / aFactor, -1 / aFactor}) → a
  8. If(abs(a) < 1, (-13.5, 13), (-15.5, 13)) → aBoxPos
  9. LaTeX(UnicodeToLetter[10007]) → xmark
  10. LaTeX(UnicodeToLetter[10003]) → cmark
  11. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  12. LaTeX("\text{Reflection in the \(x\)-axis}") → reflectionXLabel
  13. If(k < 0, "down", "up") → verTranslateWord
  14. If(h < 0, "left", "right") → horTranslateWord
  15. If(abs(a) < 1, "compression", "stretch") → verStretchCompressWord
  16. LaTeX((("\text{\vphantom{(right)}Horizontal translation " * horTranslateWord) * "}")) → horTranslateLabel
  17. LaTeX((("\text{\vphantom{compress}Vertical " * verStretchCompressWord) * "}")) → verStretchCompressLabel
  18. LaTeX((("\text{\vphantom{compress}Vertical " * verStretchCompressWord) * " by a factor of}")) → verStretchCompressLabel2
  19. LaTeX((("\text{\vphantom{(up)}Vertical translation " * verTranslateWord) * "}")) → verTranslateLabel
  20. LaTeX((("\text{\vphantom{(right)}Horizontal translation " * horTranslateWord) * " by \hspace{50} unit(s)}")) → horTranslateLabel2
  21. LaTeX((("\text{\vphantom{(up)}Vertical translation " * verTranslateWord) * " by \hspace{50} unit(s)}")) → verTranslateLabel2
  22. Textfield(textA) → ansBoxA
  23. Textfield(textH) → ansBoxH
  24. Textfield(textK) → ansBoxK
  25. If(h > 0, (-15.4, 11), (-16.1, 11)) → hBoxPos
  26. If(k > 0, (-17.5, 9), (-16.4, 9)) → kBoxPos

AI Drawing Prompt Reference

Draw a parabola on a coordinate plane with a randomly placed vertex at (h, k), vertically stretched or compressed by factor a and possibly reflected across the x‑axis. Label the horizontal translation direction (left or right), vertical translation direction (up or down), the type of vertical stretch or compression and its factor, and a note indicating reflection in the x‑axis. Provide three editable text boxes for the user to enter the values of a, h, and k, together with check‑mark and cross icons for answer feedback. The layout is clear and suited for a high‑school quadratic transformation demonstration.
The prompt above was compiled from the original drawing commands and is for reference only.