Question 904102
The given formula is a parabola with a vertex 
that is a maximum. Here's a plot:
{{{ graph( 400, 400, -1, 4, -10, 30, -16x^2 + 40x ) }}}
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When the parabola has the form:
{{{ a*x^2 +  b*x + c }}}, the x-coordinate of
the maximum is at:
{{{ -b/( 2a ) }}}
{{{ a = -16 }}}
{{{ b = 40 }}}
{{{ -b/(2a) = -40/(2*(-16) ) }}}
{{{ -b/(2a) = 40/32 }}}
{{{ 40/32 = 5/4 }}}
At {{{ t = 5/4 }}}, the height is a maximum
{{{ y[max] = -16t^2 + 40t }}}
{{{ y[max] = -16*(5/4)^2 + 40*(5/4) }}}
{{{ y[max] = -16*(25/16) + 50 }}}
{{{ y[max ] = 50 - 25 }}}
{{{ y[max] = 25 }}} ft
This matches the plot