check the picture below.
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+100}t\stackrel{\stackrel{c}{\downarrow }}{+12} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\bf \left( -\cfrac{100}{2(-16)}~~,~~12-\cfrac{100^2}{4(-16)} \right)\implies \left( \cfrac{25}{8}~~,~~12+\cfrac{625}{4}\right) \\\\\\ \left(\cfrac{25}{8}~,~\cfrac{673}{4} \right)\implies \left(\stackrel{\stackrel{\textit{took this long}}{\downarrow }}{3\frac{1}{8}}~~,~~\stackrel{\stackrel{\textit{went this high}}{\downarrow }}{168\frac{1}{4}} \right)[/tex]
