Answer
$g(x)=(x-1)^2$.
Work Step by Step
If the vertex of a quadratic function is at $(k,m)$. Then its equation can be $f(x)=\pm(x-k)^2+m$. $+$ if it is open up, $-$ if it is open down.
Hence here the function is $g(x)=(x-1)^2$.
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