Question 669843
y=400x-16x^2

 Where: y = height and x = time. 
The maximum height occurs at the vertex of the parabola whose x-coordinate  is {{{-b/2a}}} in the quadratic equation ax^2+bx+c.
 a = -16, b = 400, and c = 0. 

{{{-b/2a)= -400/-32}}}

=12.6 seconds  The time at maximum height. 

Substitute this value of x into the original equation and solve for y to get the maximum height. 

{{{y=400x-16x^2}}}
{{{y=400*12.5-16(12.5)^2}}}

=2500 feet maximum height reached by the object.

{{{drawing(500,500,-20,30,-50,2800,circle(12.5,2500,0.3),grid(1)graph(500,500,-20,30,-50,2800,y=400x-16x^2))}}}