The maximum height is the greatest value of the function, or the y-coordinate of the vertex.
[tex]f(x)=-16x^2+200x+4 \\
a=-16 \\
b=200 \\ \\
\hbox{the vertex - } (h,k) \\
h=\frac{-b}{2a}=\frac{-200}{2 \times (-16)}=\frac{-200}{-32}=\frac{25}{4} \\ \\
k=f(h)=f(\frac{25}{4})=-16 \times (\frac{25}{4})^2+200 \times \frac{25}{4} +4=\\
=-16 \times \frac{625}{16} + 50 \times 25 +4=-625+1250+4=629[/tex]
The maximum height of the arrow is 629 feet.
