Those x-intercepts aren't right. You need the quadratic formula to find the x-intercepts for this one.
To use the quadratic formula, you must have your quadratic in the form of :
which are your x-intercepts.
The domain of this function is basically all the x-values you can have which is any real number (there's not one number that will 'mess up'). For the range (the y-values the function can have), note that its vertex is at (3,-5) and opens upwards so it'll be impossible to have any y-value less than -5.