An arrow is shot into the air. a function representing the relationship between the number of seconds it
is in the air, t, and the height of the arrow in meters, ℎ, is given by
ℎ(t) = −4.9t^2 + 29.4t + 2.5.
a. complete the square for this function. show all work.
b. what is the maximum height of the arrow? explain how you know.
c. how long does it take the arrow to reach its maximum height? explain how you know.
d. what is the average rate of change for the interval from t = 1 to t = 2 seconds? compare your
answer to the average rate of change for the interval from t = 2 to t = 3 seconds, and explain the
difference in the context of the problem.
e. how long does it take the arrow to hit the ground? show your work, or explain your answer.
f. what does the constant term in the original equation tell you about the arrow’s flight?
g. what do the coefficients on the second- and first-degree terms in the original equation tell you
about the arrow’s flight?