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Parabolic Water Trajectory

Parabolic Water Trajectory
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2018-05-01 00:14
FunctionCoordinate GeometryParametric Equation
In collections Modeling real life with parabola
This example demonstrates the parabolic trajectory of water flow. It involves core math concepts like parabola, parametric curves, and coordinate geometry. Construction uses GeoGebra commands/objects: a, b, c, C, D, pic1, text1, d, e, h, g, f, text2. Suitable for high school students learning parabolas and parametric equations.

GeoGebra Commands & Parameters

  1. Numeric a(1.56)
  2. Numeric b(8.56)
  3. Numeric c(2.36)
  4. Point C(-6.9710421725755225, 7.654568573309589)
  5. Point D(-1.1214996600032303, 7.7106442008268825)
  6. Numeric d(-0.84)
  7. Numeric e(-6.91)
  8. Numeric h(-0.4)
  9. g(x) = (d * x^(2)) + (e * x) + h
  10. f(x) = ((-a) * x^(2)) - (b * x) + c

AI Drawing Prompt Reference

Draw a parabolic trajectory to demonstrate water flow, using two functions: one quadratic for the path and a parametric curve for the motion, with key points marked like the vertex and starting point, and the function expressions labeled, showing the symmetry of the parabola and the dynamic change of the parametric curve.
The prompt above was compiled from the original drawing commands and is for reference only.