The function is given to be:
[tex]h(t)=-16t^2+660t[/tex]The vertex of the parabola represents the highest (or lowest) point of a parabola. Given the normal form of a quadratic formula:
[tex]f(x)=ax^2+bx+c[/tex]the vertex is calculated to be:
[tex]x=-\frac{b}{2a}[/tex]From the function of the projectile given, we have:
[tex]\begin{gathered} a=-16 \\ b=660 \end{gathered}[/tex]Therefore, the vertex is:
[tex]t=-\frac{660}{2\times(-16)}=\frac{660}{32}=20.625[/tex]This can be confirmed by graphing the function:
Therefore, the time taken is 20.625 seconds.
