Answer
The correct graph is $C$.
Work Step by Step
The given function is
$\Rightarrow y=x^2-2x+4$
Subtract $3$ from each side.
$\Rightarrow y-3=x^2-2x+4-3$
Simplify.
$\Rightarrow y-3=x^2-2x+1$
Write the right side as the square of a binomial.
$\Rightarrow y-3=(x-1)^2$
Write in vertex form.
$\Rightarrow y=(x-1)^2+3$
The vertex is $(1,3)$. Because $a$ is positive $(a=1)$, the parabola opens up.
Hence, the correct graph is $C$.
