A grasshopper jumps off a tree stump. The height, in feet, of the grasshopper above the ground after t seconds is modeled by the function shown below. After how many seconds will the grasshopper land on the ground? Round to the nearest tenth. h(t) = -t^2 + 4/3t + 1/4A. -0.2 secondsB. 0.5 secondsC. 1.5 secondsD. 0.7 seconds

The height, in feet, of the grasshopper above the ground after t seconds is modeled by the function , which is[tex] h(t) =-t^2+\frac{4}{3}t+ \frac{1}{4} [/tex]When the grasshopper land on the ground, [tex] h(t)=0 [/tex]that is,[tex] -t^2+\frac{4}{3}t+ \frac{1}{4}=0 [/tex]Multiplying whole equation by 12 to get rid of denominators 3 and 4[tex] -12t^2+16t +3=0 [/tex][tex] (3-2t)(6t+1)=0
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3-2t=0 , 6t+1=0
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t= \frac{3}{2} , \frac{-1}{6} [/tex]And time cant be negative, so the correct option is [tex] t = \frac{3}{2}=1.5 seconds [/tex]Correct option is C .