Question

a leaf hangs from a branch 12 feet in the air. it falls to the ground at a rate of 0.25 feet per second. which graph could represent the leafs height in feet as a function of time, in seconds, after leaving the branch

Answer 1

For this case we have an equation of the form:
 $h (t) = (1/2) * (a) * (t ^ 2) + v0 * t + h0$
 Where,
 h0: initial height
 v0: initial speed
 a: acceleration
 Substituting values we have:
 $h (t) = (1/2) * (- 32) * (t ^ 2) + 0.25 * t + 12$
 Rewriting we have:
 $h (t) = -16t ^ 2 + 0.25 * t + 12$
 Note: see attached image
 Answer:
 $h (t) = -16t ^ 2 + 0.25 * t + 12$