The equation y = -16t^2 + 28t + 144 describes the height y (in feet) at time t (in seconds) of a ball tossed up in the air at 28 feet per second from a height of 144 feet from the ground. In how many seconds will the ball first reach 120 feet?
The equation is the graph of a parabola, if we start at a point above 120, then the first point that we hit 120 feet is on its way down. Note that 144 is the y-intercept so we start from there, we can only stay in quadrant one since you cannot go back in time. Plugging in 120 as y, you get 16t^2 - 28t = 24.
4t^2 - 7t = 6
Approximately 2.38 seconds