The St. Louis Arch is in the shape of a hyperbolic cosine function It is often thought that it is in the shape of a parabola, which would have a quadratic function of y = a(x-h)^2 + k, where the vertex is h, k.
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this is impossible. while the arch may appear to be a quadratic, it is in fact a hyperbolic cosine equation, a catenary. So, there is actually no way to create a quadratic to model the arch.