If a man waters his garden with a hose through which water is pumped in a pathway identified by the relation ,
where represents the horizontal distance that the water can reach in metres,
and represents the height of the water from the ground surface in metres,
find the maximum value of to the nearest centimetre.
To find the maximum value of , it is required to solve the
This equation can be solved using the quadratic formula.
In this example, , and . Therefore,
The maximum value is the positive root and evaluating on a
calculator gives m. Therefore, to the nearest
centimetre, the solution is cm.