The height h of an arrow in feet is modeled by h(t) = -16t2 + 63t + 4, where t is the time in seconds since the arrow was shot. How long is the arrow in the air?

Question

anonymous · Answer

The arrow is in the air for the length of time represented by the difference between the two values of t for which h(t) = 0 , that is, from the time its height is initially zero until its height is zero again. 
So set the function to zero and solve for t: 
-16t^2 + 63t + 4 = 0 
Factor: 
-(t - 4) (16t + 1) = 0 
t = 4 and -1/16 
So the arrow was in the air 4 - (-1/16) = 65/16 seconds. 

On the other hand, it is peculiar to have the initial time be a negative number. So looking at the formula another way, it can be described as the formula for the height of an arrow shot from an initial height of 4 feet. In that case the arrow was in the 
air for 4 - 0 = 4 seconds.

anonymous · Answer

thanks! can you help me some more please?

anonymous · Answer

sure what with