I think we are teaching mathematics the wrong way around. Instead of "this is how we solve a quadratic function; this is how we graph a function; coincidentally, the graph of a quadratic function is a parabola", start from the parabola; the quadratic function is its specification
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Obligatory link to AML: https://www.maa.org/external_archive/devlin/LockhartsLament.pdf …
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