Answer
$$\left(x-1\right)^2-4$$
Work Step by Step
Completing the square in order to write the equation in the form $a(x-h)^2+k$, we find:
$$ x^2-2x-3+\left(-1\right)^2-\left(-1\right)^2 \\ \left(x-1\right)^2-3-\left(-1\right)^2 \\ \left(x-1\right)^2-4$$
