A golfer hits a golf ball toward the hole 55 yards away. The ball follows a parabolic path given

Question

by the function h (x) = - 2 x (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 = -
25
x (x - 45)
(1 point)
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 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.

Answer 1

To solve the problem, we need to find when the golf ball hits the ground. This occurs when the height \( h(x) \) is equal to zero:

\[ h(x) = -2x(x - 45) \]

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

\[ 0 = -2x(x - 45) \]

This equation can be simplified by dividing both sides by -2:

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

Setting each factor equal to zero gives us the solutions:

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

The ball hits the ground at \( x = 0 \) (the starting point) and \( x = 45 \) yards (where it hits the ground after traveling).

Next, we need to determine how far it will roll to reach the hole, which is 55 yards away.

Since the ball hits the ground at \( x = 45 \) yards, and the hole is 55 yards away:

Distance to roll = Distance to the hole - Distance traveled when the ball hits the ground

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

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 answer 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.