Closed form solution to quadratic fit?

Is there a closed form solution to this problem? I have a set of x,y
pairs, and I would like to find the quadratic a*x^2 + b*x + c = y that
minimizes the worst case (absolute value) error between the actual data
and the quadratic approximation. I'm not trying to minimize the least
squared error, but the maximum error. Thanks.

Stephen

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