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Parabola in Standard Form

Parabola in Standard Form
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2017-04-06 10:28
FunctionCoordinate GeometryGeometric Construction
This example demonstrates a parabola in standard form. It involves key concepts of quadratic equations and coordinate geometry. Using GeoGebra commands such as Point, Line, Parabola, Segment, etc., the directrix and focus of the parabola are constructed. Suitable for high school mathematics education and learning quadratic function graphs.

GeoGebra Commands & Parameters

  1. Point(xAxis) → S_{(a,0)}
  2. Line(Z, YAxis) → Directrix
  3. Parabola(S_{(a,0)}, Directrix) → c
  4. Point(c) → P_{(x,y)}
  5. Segment(P_{(x,y)}, S_{(a,0)}) → f
  6. OrthogonalLine(S_{(a,0)}, XAxis) → g
  7. OrthogonalLine(P_{(x,y)}, Directrix) → h
  8. Intersect(c, g) → L', L
  9. Intersect(Directrix, h) → M
  10. Distance(P_{(x,y)}, S_{(a,0)}) → distanceP(x,y)S
  11. Distance(S_{(a,0)}, P_{(x,y)}) → distanceSP(x,y)
  12. Segment(P_{(x,y)}, M) → i
  13. OrthogonalLine(P_{(x,y)}, XAxis) → j
  14. Intersect(XAxis, xAxis) → B
  15. Intersect(j, XAxis) → N_{(x,0)}
  16. Intersect(c, j) → C, P'

AI Drawing Prompt Reference

Draw a parabola in standard form with focus S(a,0) and directrix. Construct the parabola c using S(a,0) and the directrix. Then take a point P(x,y) on the parabola and draw a segment f connecting P and S. Construct a perpendicular line j from P to the x-axis, intersecting at N(x,0), and find its intersection C with the parabola.
The prompt above was compiled from the original drawing commands and is for reference only.