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?

Answer 1

This describes a parabolic path that starts at x=0 on a value of y = -5.1.  That's when the rock is below ground in the hole.  To find the answer we need to know the second x axis crossing.  The first is when it is rising and reaches ground level, the second is after it peaks and falls back to the ground and lands. Using the quadratic formula I get the two zeros of this function to be about
x= 15.29, and 66.71.  The rock then lands 66.71 feet from him horizontally.