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Rotating a Parabola

Rotating a Parabola
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2013-10-16 03:33
FunctionCoordinate GeometryTransformation
This example demonstrates how to rotate the parabola [math]y=x^2[/math] by replacing variables. It showcases the concept of rotation and uses GeoGebra objects c, theangle, d, a, b to achieve this. Suitable for high school mathematics, particularly in coordinate geometry and transformations.

GeoGebra Commands & Parameters

  1. Conic c
  2. Angle theangle(0.6981317007977318)
  3. -sin(theangle) * x + cos(theangle) * y = (cos(theangle) * x + sin(theangle) * y)^(2)
  4. -sin(theangle) * x + cos(theangle) * y = 0
  5. cos(theangle) * x + sin(theangle) * y = 0

AI Drawing Prompt Reference

Draw a rotated parabola by replacing variables to demonstrate the concept of rotation, involving a parabola, an angle value, and two equation lines. Start with the original parabola, then calculate and draw the rotated parabola based on the angle, and finally use two auxiliary lines to indicate the rotation relationship.
The prompt above was compiled from the original drawing commands and is for reference only.