Question

Jamie kicked a soccer ball that traveled along a path described by the parabola y = -x^2 +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?

Answer 1

we have that
y = -x²+8x

we know that
when the ball hint the ground is the x-intercepts of the graph
the x-intercepts is for y=0
so
0=-x²+8x--------> x²-8x=0----> x*(x-8)=0

the solution is
x=0
x=8

the x intercepts are the points (0,0) and (8,0)
the distance between the x intercepts points =[8-0]-----> 8 ft

the answer is
8 ft

see the attached figure

Answer 2

The answer is 8 feet.