Question 1092505
the equation is -16t^2+110t+75, which accounts for the launch velocity and height.
-16t^2+110t+75=120
-16t^2+110t-45=0;  16t^2-110t+45
t=(1/32)(110+/- sqrt (12100-2880); sqrt 9220=96.02, use 96
t=0..4375 sec and 6.4375 sec.  Note, one uses both roots here.
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maximum height is at time t=-b/2a=110/32 or 3.44 sec. If I use exact answer or 3.4375 the height is 264.0625 feet, 264 feet. If I use 3.44 sec the height is 264 feet.
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hits ground when 16x^2-110x-75=0
x^2-110x-1200=0 divide first term by 16 and multiply last by 16
(x-120)(x+10)=0
divide constants by 16 and reduce to lowest terms
(x-(15/2))(x+(5/8))=0
move the denominator out front
(2x-15)(8x+5)=0 
Postitive root is x=7.5 seconds.
{{{graph(300,300,-2,8,-30,300,120,-16x^2+110x+75)}}}