Question 993886
it appears the rocket was in the air for 50 seconds.


your equation was h = 2t * (50 - t)


this is a quadratic equation.


when you set it equal to 0, you find the x-intercepts.


those occur at t = 0 and t = 50.


since the coefficient of the leading term is negative, the quadratic equation points up and opens down.


to see this easier, simplify the equation by multiplying the factors out.


2t * (50 - t) = 100t - t^2


reorder the terms to get h = -t^2 + 100t


the leading coefficient is negative which makes the parabola (graph of a quadratic equation is a parabola) point up (maximum point is on top) and open down.


since all value of t have the graph positive between 0 and 50, that's the time that the graph of the equation is above the x-axis which represents the time the rocket is in the air.


here's what the graph of your equation looks like:


{{{graph(600,600,-25,75,-100,1500,2x*(50-x))}}}


i used x instead of t because that's what the graphing software requires.