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

When a dolphin jumps over water surface, its trajectory follows the relation , where is the height of the dolphin above the surface, and is the horizontal distance in feet. Determine the horizontal distance covered by the dolphin starting from the moment it jumps out of the water until it dives again.

• A115 feet
• B18.4 feet
• C46 feet
• D2 feet

### Example

When a dolphin jumps over water surface, its trajectory follows the relation , where is the height of the dolphin above the surface, and is the horizontal distance in feet. Determine the horizontal distance covered by the dolphin starting from the moment it jumps out of the water until it dives again.

### Solution

The dolphin's trajectory above the water starts and ends when its height above the water is 0, i.e. when . To find the horizontal distance at these points, first set equal to 0.

Multiplying the equation by to obtain a positive coefficient of gives

Now factorise by the common factor of .

Therefore, which is the starting point of the dolphin's trajectory, or which is the end point of the dolphin's trajectory.

Therefore, the total distance travelled by the dolphin is feet.

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