A toy rocket is shot vertically into the air from a launching pad 9 feet above the ground with an initial velocity of 144 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h left parenthesis t right parenthesis equals negative 16 t squared plus 144 t plus 9h(t)=16t2+144t+9. How long will it take the rocket to reach its maximum height? What is the maximum height?