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Parabola Modeling

Parabola Modeling
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2017-11-26 02:54
FunctionCoordinate GeometryOptimizationGraphing
This example demonstrates the geometric and algebraic modeling of parabolas. It involves core math concepts like functions, coordinate geometry, and optimization. Construction highlights include GeoGebra objects: points A, B, pic1, sliders a_1, variables h, k, a, f, b, C. Suitable for high school and above students to learn function graph transformations and optimization problems.

GeoGebra Commands & Parameters

  1. Point A(-6.341999720694631, -0.18808246605521012)
  2. Point B(1.86, -0.14)
  3. Numeric a_1(3.4)
  4. Numeric h(-2.3)
  5. Numeric k(4.15)
  6. Numeric a(-0.3)
  7. f(x) = (a * (x - h)^(2)) + k
  8. Numeric b(-4.3)
  9. (b, f(b))

AI Drawing Prompt Reference

Draw a coordinate plane with a parabola whose vertex is determined by horizontal and vertical shift parameters, and whose opening direction and width are controlled by another parameter. Mark a point on the parabola with its x-coordinate given by a separate parameter, and show its y-coordinate value. Also place two fixed points, one in the lower left and one in the lower right, for reference or comparison. The graph should clearly illustrate how the parameters in the parabola equation affect its shape and position, suitable for teaching function transformations and optimization problems.
The prompt above was compiled from the original drawing commands and is for reference only.