This is the equation of a parabola. x can be any real number. domain (-∞,∞) or any real number.
The range is what y-values you can have. y values will start at the vertex and go up to infinity since it's an upward facing parabola (+a).
Vertex (-b/2a , y)
-b/2a = -2/2 =1
plug this in to find y
(-1)^2 + 2(-1) + 1 = 0
Vertex (-1, 0)
y goes from 0 to +∞
this is the range