We will convert the given equation into "vertex form"

#color(white)("XXX")y=color(green)m(x-color(red)a)^2+color(blue)b#

where

#color(white)("XXX")color(green)m# is a factor related to the horizontal spread of the parabola; and

#color(white)("XXX")(color(red)a,color(blue)b)# is the #(x,y)# coordinate of the vertex.

Given:

#color(white)("XXX")y=2x^2-4x+1#

#color(white)("XXX")y=color(green)2(x^2-2x)+1#

#color(white)("XXX")y=color(green)2(x^2-2x+color(magenta)1)+1-(color(green)2xxcolor(magenta)1)#

#color(white)("XXX")y=color(green)2(x-color(red)1)^2+color(blue)((-1))#

The vertex form with vertex at #(color(red)1,color(blue)(-1))#

Since this equation is of the form of a parabola in "standard position"

the axis of symmetry is a vertical line passing though the vertex, namely:

#color(white)("XXX")x=color(red)1#