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Parabola Construction and Properties

Parabola Construction and Properties
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2018-05-01 01:29
FunctionCoordinate GeometryGeometric ConstructionLocus
In collections Modeling real life with parabola
This example demonstrates the geometric construction of a parabola and its dynamic relationship with the focus and directrix. It involves core math concepts like parabola definition, arithmetic mean, geometric constructions, exponentiation, and intersection solving. Key GeoGebra objects used include a, b, c, f, C, D for parameterization, pic1 for visualization, and text1 for annotations. Suitable for high school coordinate geometry teaching to understand parabola properties and dynamic changes.

GeoGebra Commands & Parameters

  1. Numeric a(-0.11)
  2. Numeric b(0)
  3. Numeric c(4.7)
  4. f(x) = (a * x^(2)) + (b * x) + c
  5. Point C(-8.367443559224494, -2.0918608898061235)
  6. Point D(7.632556440775506, -2.0918608898061235)

AI Drawing Prompt Reference

Draw a parabola with its vertex near the origin, approximately at (-8.37, -2.09), and a focus on the right side, approximately at (7.63, -2.09). Use the parameters a=-0.11, b=0, c=4.7 to define the parabola equation y=ax^2+bx+c. First draw the parabola, then mark the vertex and focus.
The prompt above was compiled from the original drawing commands and is for reference only.