To solve the equation and determine how far the ball travels when it hits the ground, we start with the given equation for the height of the golf ball:
\[ h(x) = -125x(x - 45) \]
To find out when the ball hits the ground, we set \( h(x) = 0 \):
\[ 0 = -125x(x - 45) \]
This equation can be factored:
\[ 0 = -125x(x - 45) \]
Setting each factor equal to zero gives:
- \( -125x = 0 \) which implies \( x = 0 \)
- \( x - 45 = 0 \) which implies \( x = 45 \)
Thus, the ball hits the ground at two horizontal distances: \( x = 0 \) (the starting point) and \( x = 45 \) yards (when it reaches the ground again).
Since the hole is 55 yards away from the starting point, we calculate how far the ball will need to roll after hitting the ground at 45 yards:
\[ \text{Distance to hole} = 55 \text{ yards} - 45 \text{ yards} = 10 \text{ yards} \]
Therefore, the ball will hit the ground after it has traveled 45 yards and 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.