check the picture below.
[tex]\bf \textit{vertex of a vertical parabola, using coefficients}
\\\\
h=\stackrel{\stackrel{a}{\downarrow }}{-5}t^2\stackrel{\stackrel{b}{\downarrow }}{+92}t\stackrel{\stackrel{c}{\downarrow }}{+16}
\qquad \qquad
\left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\bf \left( -\cfrac{92}{2(-5)}~~,~~16-\cfrac{92^2}{4(-5)} \right)\implies \left(\cfrac{46}{5}~~,~~16+\cfrac{2116}{5} \right)
\\\\\\
\left(\cfrac{46}{5}~~,~~\cfrac{2196}{5} \right)\implies \left(\stackrel{\textit{how long it took}}{9\frac{1}{5}}~~,~~\stackrel{\textit{how high it went}}{439\frac{1}{5}} \right)[/tex]
