The height, h(x), of a punted rugby ball is given by h(x) = -1/64x^2+13/32x+2 where x is the horizontal distance in feet from the point where the ball is punted. how far, horizontally, is the ball from the kicker when it is at its highest point? (hint: examine the vertex of this quadratic function)

Given that the height of the ball has been modeled by :
h(x) = -1/64x^2+13/32x+2 
where x is the horizontal distance, then the horizontal distance of the ball when the ball is at it's highest point will be given by:
at maximum point h'(x)=0
hence:
from h(x) we get:
h'(x)=-1/32x+13/32=0
solving for x we get:
-1/32x=-13/32
thus
x=13 ft
hence at maximum point the value of x will be 13 ft