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

Equation of any Parabola is of the form y= $ax^{2}+bx+c$

If a is negative the parabola opens down.

The given equation of  soccer ball that traveled along a path was y=$-x^{2}+8x$

Comparing the two equations we have a=-1,b=8

As a is negative the parabola opens down and will have the maximum point at  vertex .

The x of vertex is given by x=$\frac{-b}{2a}$

Substituting a and b values we have:

x=$-\frac{-8}{2x1} =\frac{8}{2}= 4.$

The y of vertex is y=$(-4)^{2}+8(4) =16$

The highest point the soccer ball hit the ground is 16 ft.

Answer 2

The answer is 8 feet