A model space shuttle is propelled into the air and is described by the equation y= (-x2/2e) +ex (in 1000 ft), where y is its height in feet above the ground. What is the maximum height that the shuttle reaches?
You state that the altitude reached is defined by
y = ex - x^2/2e.
This compares to the normal expression for altitude of
h = Vo(t) - gt^2/2
where h = the maximum altitude, Vo = the initial velocity, t = the time and g = the acceleration due to gravity.
I therefore assume that your expression for the maximum altitude reached should read as
y = ex - gx^2/2
where e = the initial velocity, x = the time and g is as defined earlier.
Since you give no values for e, g or t, a specific quantitative answer is not possible.