Model the St Louis Arch with a Parabola
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This example demonstrates how to model the St Louis Arch using a parabola. It involves the core mathematical concept of a parabola. By adjusting parameters a, h, k, and c, the shape and position of the parabola can be changed. This example uses GeoGebra objects a, h, k, c, A, B, and picture pic1. Suitable for high school mathematics education, particularly for coordinate geometry and function graphing.
GeoGebra Commands & Parameters
Numeric a(1)Numeric h(0)Numeric k(0)c(x) = (a * (x - h)^(2)) + kPoint A(-2.348, -1.848)Point B(6.92, -1.98)
AI Drawing Prompt Reference
Draw a coordinate plane with an upward-opening parabola whose vertex position is controlled by three adjustable parameters for horizontal shift, vertical shift, and width. The parabola follows a quadratic function and passes through two fixed points, one on the lower left and one on the lower right, roughly at the same height. Place a background image of the St. Louis Arch for reference, so the curve echoes the arch's silhouette. Adjusting the parameters moves the parabola or changes its curvature while keeping it through the two points. The scene is clean and suitable for high school lessons on quadratic graphs and coordinate geometry.
The prompt above was compiled from the original drawing commands and is for reference only.