Question

How many times does the quadratic function below intersect the x axis?

Answer 1

`\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+7}x\stackrel{\stackrel{c}{\downarrow }}{+6} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (7)^2-4(2)(6)\implies 49-48\implies 1\qquad \stackrel{\textit{two solutions}}{\textit{two intersections}}`