Answer:[tex]2(x-2)^2-7[/tex]Step-by-step explanation:[tex]y=2x^2-8x+1[/tex]When comparing to standard form of a parabola: [tex]ax^2+bx+c[/tex][tex]a=2[/tex][tex]b=-8[/tex][tex]c=1[/tex]Vertex form of a parabola is: [tex]a(x-h)^2+k[/tex], which is what we are trying to convert this quadratic equation into.To do so, we can start by finding "h" in the original vertex form of a parabola. This can be found by using: [tex]\frac{-b}{2a}[/tex].Substitute in -8 for b and 2 for a.[tex]\frac{-(-8)}{2(2)}[/tex]Simplify this fraction.[tex]\frac{8}{4} \rightarrow2[/tex][tex]\boxed{h=2}[/tex]The "h" value is 2. Now we can find the "k" value by substituting in 2 for x into the given quadratic equation.[tex]y=2(2)^2-8(2)+1[/tex]Simplify.[tex]y=-7[/tex][tex]\boxed{k=-7}[/tex]We have the values of h and k for the original vertex form, so now we can plug these into the original vertex form. We already know a from the beginning (it is 2).[tex]a(x-h)^2+k\\ \\ 2(x-2)^2-7[/tex]