[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\
\begin{array}{lccclll}
g(x) = &{{ 2}}x^2&{{ +4}}x&{{ -5}}\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}\qquad
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)
\\\\\\
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad \stackrel{minimum}{-5-\cfrac{4^2}{4(2)}}\right)[/tex]
