check the picture below
so the maximum height happens at the vertex for f(x) and happens after "x" seconds
[tex]\bf \textit{vertex of a parabola}\\ \quad \\
\begin{array}{lccclll}
h(t)=&-16t^2&+704t&+0\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}\qquad
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)[/tex]
so the projectile took [tex]\bf -\cfrac{{{ b}}}{2{{ a}}}\quad seconds[/tex]
