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?

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 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 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 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.

GPT-4o mini · Answer

To solve the equation $ 0 = -125x(x - 45) $, let's first factor it: 1. Set the equation: $$ -125x(x - 45) = 0 $$ 2. This product is equal to zero if either factor is zero: - $ -125x = 0 $ which gives $ x = 0 $ - $ x - 45 = 0 $ which gives $ x = 45 $ So, the two solutions are $ x = 0 $ and $ x = 45 $. This means the ball hits the ground starting from $ x = 0 $ (the initial position) and also again when it has traveled $ x = 45 $ yards (when it comes back to the ground after being in the air). Now, the hole is 55 yards from the starting point. Therefore, if the ball hits the ground at 45 yards, we can calculate how much further it needs to roll to reach the hole: Distance to the hole: $$ 55 - 45 = 10 \text{ yards} $$ Thus, 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.**