When I see the quadratic formula, I flee for the hills. I hope to convince you to run with me. So that my reasons are not dismissed as the carpings of a math hater, I include a confession from first grade. Our teacher had asked what we wanted to be when we grow up. I said, “mathematician.” The teacher, using intuitive and sound Bayesian speech recognition, reflected back, “How nice that you want to be magician!”

Speaking still as a wannabe mathematician (perhaps a necessary condition for being a physicist): The quadratic formula, although a great achievement of mathematical culture,1 produces a disaster on the back of an envelope.2 Like calculus, it is a powerful, general-purpose tool. But also like calculus and elephant guns,3 it blows its targets to smithereens. From the blast fragments, an intuitive understanding is hard to assemble.

The following problem illustrates this theme....

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