Answer
graph B
Work Step by Step
$f(x)=x^2-2x-3$
$f(x)=(x^2-2x)-3$
$f(x)=(x^2-2x+(-2/2)^2)-3-((-2/2)^2)$
$f(x)=(x^2-2x+(-1)^2)-3-((-1)^2)$
$f(x)=(x^2-2x+1)-3-1$
$f(x)=(x-1)^2-4$
Vertex is $(1,-4)$
This matches with graph B.
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