Given the equation below;
[tex]y=(x-1)^2+2[/tex]We want to expand and simplify the equation;
[tex]\begin{gathered} y=(x-1)^2+2 \\ y=(x-1)(x-1)^{}+2 \\ y=(x^2-x-x+1)^{}+2 \\ y=(x^2-2x+1)^{}+2 \\ y=x^2-2x+1+2 \\ y=x^2-2x+3 \end{gathered}[/tex]Therefore, the simplified equation is;
[tex]y=x^2-2x+3[/tex]