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

A projectile was fired from a mortar cannon along a pathway that follows the relation , where represents the horizontal distance covered by the projectile in kilometers, and represents the projectile's height above the ground in kilometers. Determine the horizontal distance covered by the projectile from the moment it was fired until it hit the ground.

• A1 km
• B0.38 km
• C2 km
• D0.76 km

### Example

A projectile was fired from a mortar cannon along a pathway that follows the relation , where represents the horizontal distance covered by the projectile in kilometers, and represents the projectile's height above the ground in kilometers. Determine the horizontal distance covered by the projectile from the moment it was fired until it hit the ground.

### Solution

The end of the projectile's journey occurs when its height above the ground is equal to 0 (when ).

To find the horizontal distance at this point, first set equal to 0.

Multiplying by to obtain a positive coefficient of gives

This equation can be solved using the quadratic formula

In this example, , , and . Therefore,

The possible values of are therefore or 1.

As represents a horizontal distance, it must have a positive value. Therefore, the horizontal distance covered by the projectile is km.

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