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 = -0.005x 2 + 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

The rock will hit the ground when y=0, so we need to solve this equation for its roots. To do that, we set it equal to 0:
$0=-0.005x^{2}+0.41x-5.1$

Divide everything by -0.005 to clear out the decimals:
$0=x^{2}-82x+1020$

Now use the quadratic formula:
$x=\frac{82 \pm \sqrt{82^2-4*1020}}{2}$
$x=15.29$ or $x=66.71$
We want the larger x value since the smaller one is when the rock will reach the top of the hole.