Answer
graph B
Work Step by Step
The standard form of the given quadratic function, $f(x)=
x^2-2x-3
,$ is
\begin{array}{l}\require{cancel}
f(x)=\left( x^2-2x \right)-3
\\\\
f(x)=\left( x^2-2x+\left( \dfrac{-2}{2} \right)^2 \right)-3-\left( \dfrac{-2}{2} \right)^2
\\\\
f(x)=\left( x^2-2x+1 \right)-3-1
\\\\
f(x)=\left( x-1 \right)^2-4
.\end{array}
Since the vertex of $f(x)=a(x-h)^2+k$ is at $(h,k)$, then the vertex of the equation above is $(
1,-4
).$ Hence, it corresponds to $\text{
graph B
}.$
