Question 436896
{{{y = x^2 - 6x + 9}}}
{{{y = -x + 3}}}

{{{ graph( 500, 500, -10, 10, -10, 10, x^2 - 6x + 9, -x + 3) }}}


as you can see from the graph, intersections are at : 
(2,1) and (3,0)

let's check it:

{{{y = x^2 - 6x + 9}}}...substitute {{{y}}} with {{{-x + 3}}}

{{{-x + 3 = x^2 - 6x + 9}}}

{{{ x^2 - 6x +x - 3 + 9=0}}}

{{{ x^2 - 5x + 6=0}}}.use quadratic formula

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

{{{x = (-(-5) +- sqrt((-5)^2-4*1*6 ))/(2*1) }}} 

{{{x = (5 +- sqrt(25-24 ))/2 }}} 

{{{x = (5 +- sqrt(1))/2 }}} 

{{{x = (5 +- 1))/2 }}} 

{{{x = (5 +1)/2 }}}

{{{x = 6/2 }}}

{{{x = 3 }}}.......one solution


{{{x = (5 -1)/2 }}}

{{{x = 4/2 }}}

{{{x = 2 }}}.......another solution

now find {{{y}}}

{{{y = -x + 3}}}.......if {{{x = 3 }}}

{{{y = -3 + 3}}}

{{{y = 0}}}

{{{y = -x + 3}}}.......if {{{x = 2 }}}

{{{y = -2 + 3}}}

{{{y =1}}}

so, you get points (3,0) and (2,1) as seen on a graph