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An archer’s arrow follows a parabolic path. The height of the arrow f(x) is given by f(x) = -16x^2 + 200x + 4, in feet. Find the maximum height of the arrow.

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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.
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