A golfer hits a golf ball toward the hole 55 yards away. The ball follows a parabolic path given by the function h(x)=−1/25x(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 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 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.

Answer 1

To determine how far the ball travels when it hits the ground, we need to solve for \(x\) when \(h(x) = 0\) in the equation \(h(x) = -\frac{1}{25}x(x - 45)\).

Setting \(h(x) = 0\):

\[ 0 = -\frac{1}{25}x(x - 45) \]

We can multiply both sides by -25 to simplify:

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

This equation factors to:

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

Setting each factor to zero gives us the solutions:

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

Thus, the ball will hit the ground when it has traveled \(0\) yards (the initial position) or \(45\) yards.

Since the hole is \(55\) yards away, if the ball hits the ground after \(45\) yards, we can find the additional distance it needs to roll to reach the hole:

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

Therefore, 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.