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

A golf player hits a ball to reach a certain hole, and the relation expresses the height that the ball can reach in feet, where is the time in seconds. Determine how many seconds the ball takes to hit the ground rounding the answer to the nearest two decimal places.

• A 3.3 seconds
• B 0.75 seconds
• C 6.6 seconds
• D 1.5 seconds

### Example

A golf player hits a ball to reach a certain hole, and the relation expresses the height that the ball can reach in feet, where is the time in seconds. Determine how many seconds the ball takes to hit the ground rounding the answer to the nearest two decimal places.

• A 3.3 seconds
• B 0.75 seconds
• C 6.6 seconds
• D 1.5 seconds

### Solution

The ball will hit the ground when the value of is 0. This gives the equation

Multiplying by to obtain a positive coefficient of gives

This equation can be solved using the quadratic formula.

In this example, , and . Therefore,

The time at which the ball hits the ground will be given by the positive root. Evaluating on a calculator and rounding to the required two decimal places gives the solution seconds.

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