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

the answer is 8 feet

Answer 2

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=
`(-b)/(2a)`

Substituting a and b values we have:

x=
`-(-8)/(2x1) =(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.