Question 1179364
the maximum height is at the vertex where t=-b/2a or -17.69/-9.84 or 1.798 sec.
f(1.798)=590.90 ft.
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it reaches 0 feet when -4.92t^2+17.69t+575=0=4.92t^2-17.69t-575
t=(1/9.84)(+17.69+/-  sqrt(17.69^2+4(575)(4.92)); sqrt term=107.84
positive root is 12.76 sec rounding at end.
Domain is [0, 12.76] sec
range is [0, 590.90] m

{{{graph(300,300,-10,20,-50,700,591,-4.92x^2+17.69x+575)}}}