Question

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?

Answer 1

We are given the equation of parabola as:

$y=-x^{2} +8x$

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.

$0=-x^{2} +8x$

this is a quadratic equation, so finding gcf ,

GCF would be x here

$x(-x+8) =0$

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.

Answer 2

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!