Question 442168
Use the general form
{{{ y = m*x + b }}} where {{{ m }}} = slope
given:
{{{y = 2x - 4 }}}
The slope of a line perpendicular to this line 
has slope = {{{ -1/2 }}}
So far,
{{{ y = (-1/2)*x + b }}}
The vertex of {{{ y = x^2 - 6x + 7 }}}
is at ( -b/(2a) , y ) where
{{{ a = 1 }}}
{{{ b = -6 }}}
{{{  -(-6) / (2*1) = 3 }}}
To find the y coordinate
{{{ y = x^2 - 6x + 7 }}}
{{{ y = 3^2 - 6*3 + 7 }}}
{{{ y = 9 - 18 + 7 }}}
{{{ y = -2 }}}
Go back to:
{{{ y = (-1/2)*x + b }}}
{{{ -2 = (-1/2)*3 + b }}}
{{{ -2 = -3/2 + b }}}
{{{ 2b = -4 + 3 }}}
{{{ b = -1/2 }}}
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{{{ y = (-1/2)*x - 1/2 }}} answer
Here's the plot:
{{{ graph( 400, 400, -4, 8, -3, 10, x^2 - 6x + 7, (-1/2)*x - 1/2, 2x - 4 ) }}}