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Question

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 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 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 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 10 yards. It will need to roll an additional 45 yards to reach the hole.

Answer 1

To solve for the distance the ball will travel before it hits the ground, we can set the equation for the height of the golf ball equal to zero because when the ball hits the ground, its height will be zero:

\[ h(x) = −125x(x−45) = 0 \]

We can find the values of \( x \) that make this equation true by setting each factor equal to zero:

\[ −125x = 0 \quad \text{or} \quad (x−45) = 0 \]

Solving these equations, we get:
\[ x = 0 \quad \text{(which corresponds to the starting point, so we ignore this solution)} \]
\[ x - 45 = 0 \]
\[ x = 45 \]

The value \( x = 45 \) yards tells us that the ball will hit the ground after it has traveled 45 yards. Since the hole is 55 yards away, the ball will need to roll an additional \( 55 - 45 = 10 \) yards to reach the hole.

Therefore, 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.