Question

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), 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 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 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 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 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.

Answer 1

To determine how far the golf ball will travel before hitting the ground, we need to solve the equation:

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

This equation can be factored to find the values of \(x\):

1. Setting the equation equal to zero:
\[
-125x(x - 45) = 0
\]

2. This gives us two factors to set equal to zero:
\(x = 0\) or \(x - 45 = 0\)

3. From the second factor, we find:
\[
x = 45
\]

This means the ball will hit the ground after traveling \(45\) yards (since \(x = 0\) represents the starting point where the ball is hit).

To find out how far the ball needs to roll to make it to the hole, we subtract the distance the ball travels from the distance to the hole:

\[
\text{Distance to hole} = 55 \text{ yards}
\]
\[
\text{Distance ball travels} = 45 \text{ yards}
\]
\[
\text{Roll distance} = 55 - 45 = 10 \text{ yards}
\]

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.**