solving inequalities

Question

What is the inequality for y<x^2-2x+3

Answer 1

y=x²-2x+3 is a parabola, so y<x²-2x+3 is the area outside the parabola and excludes the parabola itself.

x²-2x+3 can be written x²-2x+1+2=(x-1)²+2, which indicates that the vertex is at (1,2). From this we can conclude that y can have any value in the open range (-∞,2). But, since y values cannot be inside the curve, y values are constrained to points outside the curve; x is unconstrained.