Landon is standing in a hole that is 5.1 ft deep. He throws a rock, and it goes up into the air, out of the hole, and then lands on the ground above. The path of the rock can be modeled by the equation y = -0.005x2 + 0.41x - 5.1, where x is the horizontal distance of the rock, in feet, from Landon and y is the height, in feet, of the rock above the ground. How far horizontally from Landon will the rock land?
A. 66.71 ft
B. 33.35 ft
C. 15.29 ft
D. 7.65 ft

Question

Landon is standing in a hole that is 5.1 ft deep. He throws a rock, and it goes up into the air, out of the hole, and then lands on the ground above. The path of the rock can be modeled by the equation y = -0.005x2 + 0.41x - 5.1, where x is the horizontal distance of the rock, in feet, from Landon and y is the height, in feet, of the rock above the ground. How far horizontally from Landon will the rock land?
A. 66.71 ft 	
B. 33.35 ft 	
C. 15.29 ft 	
D. 7.65 ft

shane_b · Answer

Set the equation equal to 0:
$$0= -0.005x^2 + 0.41x - 5.1$$Solve the quadratic and you'll get 2 values for x.  

The larger one will be point at which the rock lands...the smaller one is the horizontal point at which the rock leaves the hole.

shane_b · Answer

(and yes, the answer is in the list :)

anonymous · Answer

@Shane_B would the answer b A?

anonymous · Answer

The answer is indeed A.

anonymous · Answer

You'll see the other solution "C" is in the answers as well, but this is as the rock is on its way OUT of the hole. The later time will obviously be where the rock hits the ground.

shane_b · Answer

@chicagochica5: Yes, it's A as @qpHalcy0n  stated.