what is the domain of P(x)= x^2 - 2x + 10?

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The domain is whatever value x can be.  For your problem x can be any value (you never divide by zero, the usual limit for domains).  Your range, P(x), will be all real numbers greater or equal to 9.

  your domain (X)are all reals, and the range, which are all possible y values, are  all positive reals. Note that the X^2 is the leading term and will dominate the answer. No matter how large your X in negative value, it will be square and turns into a very large number. Or, if it is a very small negative number,the constant term 10 will cover it.