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) = −
1
25
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 = −
1
25
x(x − 45)
(1 point)
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 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 10 yards. It will need to roll an additional 45 yards
to reach the hole

Answer 1

To determine how far the golf ball will have traveled when it hits the ground, we need to solve the equation given for \( h(x) \):

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

We can start by factoring out the constant -\(\frac{1}{25}\):

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

Now, we can set each factor equal to zero to find the possible values for \( x \):

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

So, the solutions to the equation are \( x = 0 \) and \( x = 45 \).

This means the ball hits the ground at a horizontal distance of 45 yards.

Next, to determine how far the ball will need to roll to reach the hole, we can subtract the distance the ball traveled from the distance to the hole:

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

Hence, the ball will need to roll an additional 10 yards to reach the hole.

The final 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.