[tex]\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+2} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\stackrel{\textit{one intercept}}{\textit{\underline{one solution}}}\qquad \\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ 4^2-4(2)(2)\implies 16-16\implies 0[/tex]
