Question

an achers arrow follows a parabolic patch. the height of the arrow, f(x), in feet, can modeled by the function f(x)=-0.07x^2+1.5x+6.7, where x is the arrows horizontal distance, in feet. what is the maximum height of the arrow?

Answer 1

The maximum height of the arrow is 14.73 m.

Explanation:

The height of the arrow follows a parabolic path. Its height can be modeled by the function,

`f(x)=-0.07x^2+1.5x+6.7` ......(1)

It is required to find the maximum height of the arrow

For maximum height,
`f'(x)=0`

i.e.

`(d(-0.07x^2+1.5x+6.7))/(dx)=0\\\\-0.14x+1.5=0\\\\0.14x=1.5\\\\x=(1.5)/(0.14)\\\\x=10.71\ m`

Put x = 10.71 m in equation (1). So,

`f(x)=-0.07(10.71)^2+1.5(10.71)+6.7\\\\f(x)=14.73\ m`

So, the maximum height of the arrow is 14.73 m.