How to calculate the error of a taylor polynomial in multivariable

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So I've tried googling but I am not finding any information about the error in mulitvariable, everything out there is about single variable. In my prof powerpoint it says for quadratic approximation of two variabless: $f(x,y) - Q(x,y) = O((\sqrt{(x − a)^2 + (y − b)^2})^3)$

I can't find any other information. But this big-O notation doesn't help me calculate the error tho? It only tells me how the error will look like, as in it works as a bound. How do I calculate the actual error of quadratic approximation for example? Is there any proof I can look at?

Thanks beforehand.