# 9.6.2. Solving a Second-Degree Equation in One Unknown Algebraically and Geometrically

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.

• Acm
• Bcm
• Ccm
• Dcm

### Example

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.

### Solution

To find the maximum value of , it is required to solve the equation

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.

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