Question 89374
The x-intercepts are where y = 0
{{{y = x^2 - 2x + 4}}}
{{{x^2 - 2x + 4 = 0}}}
{{{x^2 - 2x = -4}}}
add 1 to both sides
{{{x^2 - 2x + 1 = -4 + 1}}}
{{{(x-1)^2 = -3}}}
I need to take the square root of both sides, but
I can't because the square root of -3 is imaginary,
so there are no x-intercepts
Here is the graph. You can see that it never touches 
the x-axis
{{{ graph( 400, 400, -5, 10, -5, 20, x^2 - 2x + 4) }}}