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 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.
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.

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 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.
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Answer 1

To solve the equation \(0 = -125x(x - 45)\), we can first factor it.

Setting the equation to zero, we have: \[ -125x(x - 45) = 0 \]

This product is zero if either factor is zero. Therefore, we solve for \(x\):

1. \(x = 0\) (which corresponds to the starting point where the ball is hit)
2. \(x - 45 = 0 \Rightarrow x = 45\) (which corresponds to the point where the ball hits the ground)

Now, the ball travels a distance of \(45\) yards horizontally when it hits the ground.

The hole is \(55\) yards away. To find out how far the ball needs to roll to make it to the hole, we subtract the distance the ball has already traveled from the distance to the hole: \[ \text{Distance to hole} - \text{Distance traveled} = 55 - 45 = 10 \text{ yards} \]

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.

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.