The height above ground in feet of a toy rocket launched upw

The height above ground, in feet, of a toy rocket launched upward from the top of a building is given by s(t) = 16t2 + 64t + 192.

(a) What is the height of the building? ft

(b) What is the maximum height attained by the rocket? ft

s(t) = -16t^2 + 64 t + 192

a) for height of the building plug t = 0

s(t) = -16(0)^2 + 64(0) + 192

s(t) = 192 feet

height of the building = 192 feet

b) maximum height is the vertex of the equation

plug t = -64 / 2*-16 = 2 in the equation

-16(2)^2 + 64(2) + 192 = 256 feet

maximum height = 256 feet

c) time when rocket strikes tyhe ground plug s(t) = 0 and solve for t

-16t^2 + 64 t + 192 = 0

or dividing the entire equatio by -16

t^2 - 4t - 12 = 0

( t - 6 ) ( t+ 2) = 0

t = 6 seconds

rocket strikes the ground after 6 seconds