Question

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.

Answer 1

The maximum height is the greatest value of the function, or the y-coordinate of the vertex.


`f(x)=-16x^2+200x+4 \\ a=-16 \\ b=200 \\ \\ \hbox{the vertex - } (h,k) \\ h=(-b)/(2a)=(-200)/(2 * (-16))=(-200)/(-32)=(25)/(4) \\ \\ k=f(h)=f((25)/(4))=-16 * ((25)/(4))^2+200 * (25)/(4) +4=\\ =-16 * (625)/(16) + 50 * 25 +4=-625+1250+4=629`

The maximum height of the arrow is 629 feet.