During halftime of a football game, a sling shot launches T-shirts at the crowd. A T-shirt is launched from a height of 4 feet with an initial upward velocity of 80 feet per second. The T-shirt is caught 50 feet above the field. How long will it take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time?