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Vertical Translations of Parabolas

Vertical Translations of Parabolas
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2018-11-07 03:51
FunctionTrigonometryTransformation
This example demonstrates the vertical translation of parabolas. Key mathematical concepts include quadratic equations and transformations. By adjusting parameters, you can observe the vertical movement of the parabola. Mainly using GeoGebra commands such as Zip, Element, SelectedIndex, Flatten, Point, Polygon, Sequence, Textfield, UnicodeToLetter, If, etc. Suitable for high school mathematics education and learning the graphical transformations of quadratic functions.

GeoGebra Commands & Parameters

  1. Zip(abs(A), A, kValsNumeric) → kValsAbsolute
  2. Element(kValsNumeric, index + 1) → k
  3. Element(kValsAbsolute, index + 1) → absK
  4. SelectedIndex(dropDown) → selectedTranslation
  5. Flatten(Sequence[Sequence[(i, j), i, -3, 3, 0.5], j, -9, 9, 0.5]) → gridSpace
  6. Point(gridSpace) → E
  7. Point(gridSpace) → A
  8. Point(gridSpace) → B
  9. Point(gridSpace) → C
  10. Point(gridSpace) → D
  11. Zip((A, image(A)), A, xValues) → pointsImage
  12. Zip((A, original(A)), A, xValues) → pointsOriginal
  13. Polygon({(-3.5, 9.5), (3.5, 9.5), (3.5, -9.5), (-3.5, -9.5)}) → background
  14. Sequence(Line[(i, 0), yAxis], i, -3.5, 3.5, 1) → gridLinesVertical
  15. Sequence(Line[(0, i), xAxis], i, -9.5, 9.5, 1) → gridLinesHorizontal
  16. Textfield(unitsText) → inputUnits
  17. UnicodeToLetter(10003) → checkmark
  18. UnicodeToLetter(10007) → xmark
  19. If(isCorrectWholeThing, checkmark + " Correct!", xmark + " Incorrect") → verdict