Question

What is the domain of "p" when p(x)=x squared-2x+4

Answer 1

write exponents this way:

p(x) = x^2 - 2x + 4

since "p" is the dependent variable, we usually use the word "range" instead of domain.
Domain would be your choice of the independent variable, that is, the x in this case.

anyway...
the x of the vertex is -b/(2a) for f(x) = ax^2 + bx + c

so the x of the vertex is 2/2 = 1
p(1) = 1-2+4 = 3

so the range of the function is p(x) ≥ 3