Have you ever been on or seen a ride like this at a fair or amusement park? Imagine being strapped into your seat at the bottom of this 350-foot tower,
with your feet dangling just above the ground. You make the trip up the
tower at a steady rate of 20 feet per second, stop at the top of the tower to
hang for a few seconds, then suddenly drop in a free fall for 288 feet!
The trip up the tower is a linear relationship. The height of the riders, h, is
equal to the constant rate multiplied by the time, t, since they began the
trip up.
The free fall down the tower is a quadratic relationship. The distance from
the top to the bottom of the free fall, d, is modeled by this equation, where
t is the time since the free fall began and do is the initial distance above the
bottom of the free fall.
d = -16t2 + do
Write an equation representing each relationship.