Question

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

Answer 1

Maximum of function
`f(x)=ax^2+bx+c` where
`a \\eq 0` you can find by using this formula:
`y_(\max)= - (\Delta)/(4a)=-(b^2-4ac)/(4a)=(4ac-b^2)/(4a)=c-(b^2)/(4a)`

In height function you've got:

a= -16
b= 200
c= 4

Just substitute! You'll get


`y_(\max) = 4 - (200^2)/(4 \cdot (-16))=4-(40 \ 000)/(-64)=4+(40 \ 000)/(64)=4+625=629`

Maximum height is 629 [units]