Equation of any Parabola is of the form y= [tex]ax^{2}+bx+c[/tex]
If a is negative the parabola opens down.
The given equation of soccer ball that traveled along a path was y=[tex]-x^{2}+8x[/tex]
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=[tex]\frac{-b}{2a}[/tex]
Substituting a and b values we have:
x=[tex]-\frac{-8}{2x1} =\frac{8}{2}= 4.[/tex]
The y of vertex is y=[tex](-4)^{2}+8(4) =16[/tex]
The highest point the soccer ball hit the ground is 16 ft.
