.
The path of water from a hose on a fire tugboat can be approximated by the equation y = −0.0045x^2 + 1.25x + 5,
where y is the height, in feet, of the water above the ocean when the water is x feet from the tugboat.
When the water from the hose is 7 feet above the ocean, at what distance from the tugboat is it?
~~~~~~~~~~~~~~~
Write equation as you read the problem
−0.0045x^2 + 1.25x + 5 = 7.
From the equation
0.0045x^2 - 1.25x - 5 = -7,
0.0045x^2 - 1.25x + 2 = 0.
Use the quadratic formula
= = = .
There are two roots
= = 1.61 ft (in ascending branch). ANSWER
and
= = 276.27 ft (in desceding branch). ANSWER
Solved.