Question 811506
complete the square
{{{ax^2 + bx + c}}}
{{{ax^2 + bx + ((1/2)b)^2 - ((1/2)b)^2 + c}}}
{{{(x + (1/2)b)^2 + c - ((1/2)b)^2}}}

That probably looks a little complicated, so i will explain it.
{{{y = x^2 + 8x + 1}}}
take half of 8 (4)
and square it. (4*4)
then add and subtract it into the equation
{{{y = x^2 + 8x + 16 - 16 + 1}}}
now take {{{(x^2 + 8x + 16)}}}
this can be factored into
{{{(x+4)^2}}}
then you just add on the rest
{{{(x+4)^2-15}}}
this is the vertex form
and your vertex is (-4,-15)