Question 822060
y is squared, x is only power 1.  This is a horizontal parabola.  You want a finished form like {{{x=a(y-k)^2+h}}}, and you find it through completing the square for the y.


{{{y^2= -4y+2x+1}}}
{{{y^2+4y-1=2x}}}
{{{2x=y^2+4y-1}}}
The missing square piece, or term, is 4.
{{{2x=y^2+4y+4-4-1}}}
{{{2x=(y+2)^2-5}}}
{{{highlight(x=(1/2)(y+2)^2-5/2)}}}


The formula for x could have been found without leaving the 2 factor with the x, but keeping the 2x allowed an easier completion of the square process.