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Vertical Parabola

Vertical Parabola
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2017-08-01 03:09
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the geometric construction of a vertical parabola. Key mathematical concepts include the parabola, vertex, focus, and directrix. Using GeoGebra commands such as Point, OrthogonalLine, and Intersect, the generation process of the parabola can be dynamically shown. Suitable for high school mathematics education, particularly in coordinate geometry and function graphs.

GeoGebra Commands & Parameters

  1. Point(Directrix) → A
  2. OrthogonalLine(A, Directrix) → l
  3. Intersect(Parabola, l) → B,
  4. Segment(A, B) → d_1
  5. Segment(B, Focus) → d_2
  6. Line(Focus, Vertex) → Axis
  7. OrthogonalLine(Focus, Axis) → b
  8. Intersect(Parabola, b) → C, D
  9. Segment(D, C) → LR

AI Drawing Prompt Reference

Draw a vertical parabola with its vertex, focus, and directrix clearly marked. Pick a point on the directrix, construct a perpendicular line from this point to the directrix, and let it meet the parabola at a point. Connect this intersection point to the directrix point and to the focus, showing equal distances. Draw the axis through the focus and vertex, then a perpendicular line through the focus to the axis, intersecting the parabola at two points. Connect these two points to form the latus rectum, illustrating the key geometric features of the parabola.
The prompt above was compiled from the original drawing commands and is for reference only.