Domain is the set of x values for which the function is defined.
In this function, any value of x will evaluate to a number. Thus the domain of the function is all the real numbers.
As for the range - this is the set of values y can get.
The function is a parabola. Since the coefficient of x^2 is positive, this function has a minima (The maximal value is infinity - just plug in x=infinity or x=-infinity and you'll see).
To calculate the minima, we take the first derivative with respect to x and equate it to zero: