The domain of a quadratic function in standard form is always all real numbers, meaning you can substitute any real number for x. The range of a function is the set of all real values of y that you can get by plugging real numbers into x.
If the quadratic is in the form of y = x^2 then the statement is correct. The entire family all have a domain of all the real numbers.
However if the quadratic is of the form x=y^2 then the starting point of this quadratic is (0,0). All of these quadratics have a different starting point. \\
Since you have not specified the kind of quadratic, the answer is not always true.
