[tex]Standard\ form:f(x)=ax^2+bx+c\\--------------------\\f(x)=2(x-1)^2+3=2(x-1)(x-1)+3\\\\=2[(x)(x)+(x)(-1)+(-1)(x)+(-1)(-1)]+3\\\\=2(x^2-x-x+1)+3=2(x^2-2x+1)+3|use\ distributive\ property\\\\=2x^2-4x+2+3=\boxed{2x^2-4x+5}\\\\Answer:\boxed{f(x)=2x^2-4x+5}[/tex]
