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Parabola Modeling: Gateway Arch St. Louis (by Sofia S)

Parabola Modeling: Gateway Arch St. Louis (by Sofia S)
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2018-05-01 03:32
FunctionCoordinate GeometryGeometric ConstructionSlider AnimationGraphing
In collections Modeling real life with parabola
This GeoGebra example demonstrates how to model the iconic Gateway Arch in St. Louis, Missouri, using a parabola, turning a real-world architectural structure into a mathematical representation. The core mathematical concept is the quadratic function (parabola) and its graph, along with the comparison between a function curve and an embedded photograph. Construction highlights: the image object pic1 imports the arch photo; points C and D define key positions; parameters a, b, c control the parabola equation f; text1 and text2 display labels and explanations. Suitable for middle or high school students learning quadratic functions, coordinate geometry, or mathematical modeling, and for interdisciplinary projects linking math and architecture. By adjusting sliders or parameters, learners can visually explore how the parabola's opening, vertex, and width align with the arch's silhouette, deepening their understanding of how mathematics shapes real-world design.

GeoGebra Commands & Parameters

  1. Numeric a(-0.81)
  2. Numeric b(0.1)
  3. Numeric c(1.3)
  4. f(x) = (a * x^(2)) + (b * x) + c
  5. Point C(-5, -5)
  6. Point D(5, -5)

AI Drawing Prompt Reference

Draw a coordinate plane with a downward-opening parabola whose equation is controlled by three parameters, currently set to make the vertex near the vertical axis and the opening relatively narrow. Place two points symmetrically below the horizontal axis on the left and right sides to mark the arch's base positions. Include an embedded photo of the Gateway Arch as a background reference, with its silhouette roughly matching the parabola. Add text labels showing the quadratic equation form and explanatory notes about how the parabola models the arch's shape. The overall composition should clearly show the comparison between the mathematical curve and the real architectural photo.
The prompt above was compiled from the original drawing commands and is for reference only.