On Intuition and the Quadratic Equation

By Wes Carroll, founder of Wes Carroll Tutoring and Consulting

“Dr. Po-Shen Loh has discovered a new way to solve quadratics.”
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Well, yes and no. Dr. Loh is a great coach, educator, and evangelist, and I admire and respect him. If he says he was “dumbfounded,” then there’s something there.

The thing is, though, that the press is making a big thing about the “new formula he’s discovered”.  That’s just plain incorrect: the interesting part here isn’t the formula. That formula is just shoehorning a simple idea into the language of math, and in this instance the language is almost as cumbersome as with the original, better-known formula. So, not an improvement.

No, the key idea here is in putting together two facts:
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• that the roots of a quadratic are equidistant from the centerline of its graph
• that that allows one to systematically work out the roots of a quadratic without either guessing or an explicit formula

Taught well, this new method will relieve students of the need to memorize any formula per se.  Instead, students who understand this will follow the method intuitively, and will wonder why quadratics get so much careful attention in math texts: instead, they’ll just be obvious. (Now that is a development worth writing about.)

Update: my colleague Megan deVries of bodsat.com notes that the SAT tests the concept of the equidistant pairs regularly since the redesign.
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