Question

The path of water from sprinkler is modeled by h(d) = -2*d^2 + 6*d + 4 where h(d) is the height of the water in feet at a distance of d feet from the jet. How far from the sprinkler does the water hit the ground.

Answer 1

Explanation:

When the water hits the ground, the height of it is 0. So replace h(d) with 0 and factor the quadratic. I used the quadratic formula:

`d=(-6+/-√(36-4(-2)(4)) )/(-4)` so

`d=(-6+/-√(36+32) )/(-4)` and

`d=(-6+/-√(68) )/(-4)` which gives us the two distances as

`d=(-6+√(68) )/(-4)` and
`d=(-6-√(68) )/(-4)`

The first case gives us a distance of -.56155 feet and the second a distance of 3.56155 feet. Since distance will never be negative, then

d = 3.56 feet