Question 862688
{{{ f(x) = -8x^2 + 16x + 10 }}}
When the equation has the form 
{{{ f(x) = ax^2 + b*x + c }}}, the maximum
occurs at {{{ x[max] = -b / (2a) }}}, so
{{{ x[max] = -16 / ( 2*(-8)) }}}
{{{ x[max] = 1 }}}
Plug this back into the equation to find
{{{ f( x[max] ) }}}
{{{ f(1) = -8*1^2 + 16*1 + 10 }}}
{{{ f(1) = -8 + 16 + 10 }}}
{{{ f(1) = 18 }}}
The time to reach the maximum height is 1 sec
The maximum height is 18 ft
Here's the plot:
{{{ graph( 400, 400, -1, 3, -2, 22, -8x^2 + 16x + 10 ) }}}