A rock is tossed from a platform and follows a parabolic path through
the air. The height of the rock in metres is given by h(t)=-5t^2 + 12t + 14, where t is measured in seconds.
b) How long is the rock in the air?
c) For what times is the height of the rock greater than 17 m?
d) How long is the rock above a height of 17 m?

Question

A rock is tossed from a platform and follows a parabolic path through
the air. The height of the rock in metres is given by h(t)=-5t^2 + 12t + 14, where t is measured in seconds.
b) How long is the rock in the air?
c) For what times is the height of the rock greater than 17 m?
d) How long is the rock above a height of 17 m?

anonymous · Answer

b) Find the zeros of the parabola equation. These zeros tell you when the rock is at ground level and at what time. That would tell you how long the rock was in the air. 

c) solve for t for when 17=-5t^2 + 12t + 14: there should be 2 answers when the rock starts above 17m and when it drops below, 

d) subtract the smaller time in (c) from the larger time in (c)