The given expression is
[tex]y=x^2-2x+2[/tex]
First, we find the vertex (h,k) where a = 1, b = -2, and c = 2.
[tex]\begin{gathered} h=-\frac{b}{2a}=-\frac{-2}{2\cdot1}=1 \\ k=f(1)=(1)^2-2(1)+2=1-2+2=1 \end{gathered}[/tex]
So, the vertex is at (1,1), the vertex form would be
[tex]y=(x-1)^2+1[/tex]
The expression has minium (1,1), its opening upside and it doesn't have intercepts.
The image below shows the graph
Hence, the previous analysis was correct.
