Question 967783
p is a variable.  x is a different variable.  Still, a quadratic inequality in x.  Reaching the appropriate stage of Intermediate Algebra, one would judge that the quadratic expression can represent a parabola opening upward and has a vertex as a minimum.    f(x)=x^2-2x+p-3 may be completely above the horizontal axis, or touches the horizontal axis at exactly one point, or CROSSES the horizontal axis at two points.  Which case occurs depends on the value of p.