Question 1117051
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-5t^2 + 15t + 12 = 22


-5t^2 + 15t + (12-22) = 0


-5t^2 + 15t - 10 = 0


Discriminant of the equation  d = 15^2 - 4*(-5)*(-10) = 225 - 200 = 25


{{{t[1,2]}}} = {{{(-15 +- sqrt(25))/(2*(-5))}}} = {{{(-15 +- 5)/(-10)}}}.


The two roots are  


{{{t[1]}}} = {{{(-15+5)/(-10)}}} = {{{(-10)/(-10)}}} = 1   and


{{{t[2]}}} = {{{(-15-5)/(-10)}}} = {{{(-20)/(-10)}}} = 2.


<U>Answer</U>.  {{{t[1]}}} = 1 second on the way up,   and  {{{t[2]}}} = 2 second on the way down.


{{{graph( 330, 330, -2.5, 5.5, -2.5, 30.5,
          -5x^2 + 15x + 12, 22
)}}}


Plot y = {{{-5t^2 + 15t + 12}}} (red) and y = 22 (green)


You consider the plot at t >= 0.
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