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Giải thích các bước giải:

$\text{xét }y = x^2 - 2x - 3 = f(x)\\f'(x) = 2x - 2\\f'(x) = 0\\\Leftrightarrow x = 1\\ \text{ta có BBT $f(x)$ :} \\\begin{array}{|c|cc|}\hline \text{$x$}&\text{$-\infty$}&\text{}&\text{}1&\text{}&\text{}&\text{$+\infty$}\\\hline \text{$f'(x)$}&\text{}-&\text{}&\text{}0&\text{}&\text{}&+\\\hline \text{$f(x)$}&+\infty&\text{}&\text{}&\text{}&\text{}+\infty&\text{}\\&\text{}&\text{$\searrow$}&\text{}&\text{}\nearrow&\text{}&\text{}\\&\text{$$}&\text{}&\text{}-4&\text{}&\text{}&\text{}\\\hline \end{array}\\f(x)=0\\\Leftrightarrow \left[\begin{matrix} x = -1\\ x = 3\end{matrix}\right.\\ \text{ta có BBT $\left|f(x)\right|$ :}\\ \begin{array}{|c|cc|}\hline \text{$x$}&\text{$\infty$}&\text{}&\text{}0&\text{}&\text{}2&\text{}&\text{$+\infty$}&\text{}&\text{}\\\hline\text{$\left|f(x)\right|$}&\text{}+\infty&\text{}&\text{}&\text{}&\text{}4&\text{}&\text{}&\text{}&\text{}+\infty\\&\text{}&\text{$\searrow$}&\text{}&\text{}\nearrow&\text{}&\text{}\searrow&\text{}&\text{}\nearrow\\&\text{$$}&\text{}&\text{}0&\text{}&\text{}&\text{}&\text{}0\\\hline \end{array}\\\mathscr{X_{\textit{in hay nhất}}}$