We are given the equation of parabola as:
[tex] y=-x^{2} +8x [/tex]
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.
[tex] 0=-x^{2} +8x [/tex]
this is a quadratic equation, so finding gcf ,
GCF would be x here
[tex] x(-x+8) =0 [/tex]
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
Answer: The Soccer Ball hit the ground 8 feet away from Jamie.
The given function of parabola is:
y =-x² + 8x
Where y = height in feet and x = horizontal distance in feet.
When the soccer ball hit the ground then height will be 0.
So, we need to find x when y=0. So, plug in y=0 in the given equation and then solve for x. Therefore,
-x² + 8x =0
x (-x + 8)=0 Taking x as a common factor from each terms.
So, x =0 and -x + 8 = 0 Set up each factors equal to 0.
-x = -8
x = 8
So, x = 0 and x = 8
From the above result we can say that, at the starting point when x=0 then y =0 and y is also 0 at x = 8.
So, the soccer ball hits the ground when the horizontal distance is 8 feet.
Hope this helps you!