when the parabola crosses the x-axis the parabola "intersects" or touches the x-axis, and therefore is an x-intercept, and we can get those by simply setting y = 0 and getting "x".
[tex]\bf y=x^2-2x-3\implies \stackrel{y}{0}=x^2-2x-3\implies 0=(x-3)(x+1)
\\\\\\
x=
\begin{cases}
3\\
-1
\end{cases}[/tex]
