Question 123950
To find the x-intercepts, set y equal to zero 



{{{x^2-4x+4=0}}} 


{{{(x-2)(x-2)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{x-2=0}}} or  {{{x-2=0}}} 


{{{x=2}}} or  {{{x=2}}}    Now solve for x in each case



Since we have a repeating answer, our only answer is {{{x=2}}}


Notice if we graph {{{y=x^2-4x+4}}}  we can see that the only root is {{{x=2}}}. So this visually verifies our answer.



{{{ graph(500,500,-10,10,-10,10,0, x^2-4x+4) }}}