Question 1064461
The formula for vertex ( minimum in this case ) 
is {{{ x[v] = -b/(2a) }}}
when the general form is:
{{{ f(x) = a*x^2 + bx + c }}}
{{{ a = 1 }}}
{{{ b = 2 }}}
{{{ x[v] = -2/(2*1) }}}
{{{ x[v] = -1 }}}
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{{{ f(-1) = (-1)^2 + 2*(-1) + c }}}
{{{ f(-1) = 1 - 2 + c }}}
given:
{{{ f(-1) = sqrt(2) }}}
{{{ sqrt(2) = -1 + c }}}
{{{ c = 1 + sqrt(2) }}}
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Here's the plot:
{{{ graph( 400, 400, -5, 5, -5, 5, x^2 + 2x + 1 + sqrt(2) ) }}}