H(t)=-t^2+12t+5

Question

what is the intial height of the rocket?

When does the rocket hit the ground(round answer in 3 different ways?

For how long does the rocket have a height of more than 35 meters (3 significant figuers)

Answer 1

initial height = 5 = h(0)

it hits the ground when -t^2 + 12t +5 = 0

t^2 -12t -5 = 0

t = 12/2 + (1/2)sqr(144+20)

= 6 + (1/2)sqr164 = about 6 +6.4 = 12.4 seconds

35=-t^2 +12t +5

t^2 -12t +30

t = 12/2 + or - (1/2)sqr(144-120) = 6+ or -2.45 = 3.55 or 8.45

8.45 -3.55 = 4.9 seconds it's above 35 meters

to be more realistic the t^2 term should have had a coefficient of -4.9. Possibly it's a typo. IF so, you get a different answer.