I was mucking about and trying to prove a quadratic was continuous at all arbitrary points c but got stuck when trying to find a suitable upper bound for $\vert x-c\lvert$. The function was $x^2+2x-8$ and my last line is $\vert f(x)-f(c)\vert=\vert x-c\vert\vert x+c+2\vert$. I can't find an upper bound that won't cause problems when I adjust the factor and take its absolute value. Any clues on how to proceed? Thanks.
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$|x+c+2| = |x-c+2c+2|\le|x-c|+2|c+1|$. – amsmath Oct 08 '19 at 18:20
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https://math.stackexchange.com/questions/2378632/proof-that-fx-x2-is-continuous-delta-epsilon – Fede1 Oct 08 '19 at 20:41