Steve S. answered • 04/06/14

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Tutoring in Precalculus, Trig, and Differential Calculus

h = -16t^2 + 78t = -2t(8t - 39)

Zeros: t = 0 and t = 39/8

Axis of Symmetry and Vertex at t = 39/8/2 = 39/16.

h(39/16) = -2(39/16)(8(39/16) - 39)

= -(39/8)(39/2 - 39)

= -(39/8)(-39/2) = 39^2/4^2 = (39/4)^2

= ((40-1)/4)^2 = (10 - 1/4)^2

= 100 - 5 + 1/16 = 95 + 1/16 > 80

Yes, the rocket will reach and exceed a height of 80 meters.