Shouldnt we also specifiy for the domain that x=all real numbers if a does not equal 0 since x=-b over 2a and we cant have a demonator as 0?

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The formula x = -b/2a is for finding the axis of symmetry and x-coordinate of the vertex.  It has nothing to do with the domain.  The domain of ALL quadratic functions is all real numbers, since they are continuously opening to the left and right.If a = 0, then y = c, which is the equation of a horizontal line.  All non-vertical lines also have a domain of all real numbers.