A golfer hits a golf ball toward the hole 55 yards away. The ball follows a parabolic path given by the function h(x)=−125x(x−45)

Question

, where h(x)
is the height of the golf ball and x is the horizontal distance it has traveled. Solve the equation to determine how far the ball will have traveled when it hits the ground. How far will the ball need to roll to make it to the hole?

0=−125x(x−45)


(1 point)
Responses

The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.
The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.

The ball will hit the ground after it has traveled 25 yards. It will need to roll an additional 30 yards to reach the hole.
The ball will hit the ground after it has traveled 25 yards. It will need to roll an additional 30 yards to reach the hole.

The ball will hit the ground after it has traveled 10 yards. It will need to roll an additional 45 yards to reach the hole.
The ball will hit the ground after it has traveled 10 yards. It will need to roll an additional 45 yards to reach the hole.

The ball will hit the ground after it has traveled 30 yards. It will need to roll an additional 25 yards to reach the hole.

Answer 1

To solve the equation \(0 = -125x(x - 45)\), we can set the equation equal to zero and factor it:

\[ 0 = -125x(x - 45) \]

This equation will equal zero when either \(x = 0\) or \(x - 45 = 0\). Thus, we can find the solutions:

1. \(x = 0\)
2. \(x - 45 = 0 \Rightarrow x = 45\)

The solutions indicate that the ball hits the ground at \(x = 0\) yards (initial position) and at \(x = 45\) yards.

To find out how far the ball needs to roll to reach the hole (which is 55 yards away), we can calculate the distance the ball needs to roll after it hits the ground:

\[ \text{Distance to hole} = 55 \text{ yards} - 45 \text{ yards} = 10 \text{ yards} \]

Thus, the ball will hit the ground after it has traveled 45 yards, and it will need to roll an additional 10 yards to reach the hole.

So the correct response is:

The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.