Jamie kicked a soccer ball that traveled along a path described by the parabola y = -x2 +8x, where y equals the height of the soccer ball in feet, and x = the horizontal distance in feet that the ball has traveled from jamie. how many feet from jamie does the soccer ball hit the ground?

We are given the equation of parabola as:

Here y is height of soccer ball in feet and x is the horizontal distance in feet

Now when the ball will hit the ground , the height will become zero.

So plugging y as 0 in the given equation and solving for x , that will give us the distance traveled by soccer ball.

this is a quadratic equation, so finding gcf ,

GCF would be x here

now equating each part equal to zero,

we have either x=0 or -x+8=0

solving -x+8=0 we get x=8

as distance traveled cannot be zero so we say that x=8 is the answer

The Soccer Ball hit the ground 8 feet away from Jamie.