Question 1126994

{{{h(t)=-16t^2+120t+3}}}

 When is the potato {{{203}}} feet in the air means {{{h(t)=203}}}

{{{203=-16t^2+120t+3}}}........solve or {{{t}}}; I am going to move all terms from the right to the left

{{{16t^2- 120t+203-3=0}}}

{{{16t^2- 120t+200=0}}}...factor out {{{8}}}

{{{8(2t^2- 15t+25)=0}}}....to factor rest, write {{{-15t}}} as {{{-5t-10t}}}  

{{{8(2t^2- 5t-10t+25)=0}}}.....group

{{{8((2t^2- 5t)-(10t-25))=0}}}....actor out {{{t}}} from first group and {{{5}}} from second group 
{{{8(t(2t- 5)-5(2t-5))=0}}}

{{{8 (t - 5) (2t - 5) = 0}}}

=> {{{t=5/2=2.5s}}} or {{{t=5s}}}

The potato is {{{203}}} feet in the air after {{{2.5}}} second on the way up and after {{{5 }}}seconds on the way back down.