we are using the quadratic formula in class. Im just a bit confused how to apply it to word problems.

Question

a firework is launched upward at an initial velocity of 116 feet per second from a cliff 300 feet above a beach. What is the height of the firework after 2 seconds? At what time(s) is the object 350 feet above the ground?

Answer 1

The quadratic you need is $s(t)=300+116t-16t^2$ where $16t^2$ is the acceleration due to gravity and it is subtracted because as written s(t) is distance in the up direction whereas gravity acts downward.

s(2) = the height after 2 seconds (and I'll let you figure that)

The answer to the second part is 350 = s(t) = $300+116t-16t^2$ ... and this is where you need the quadratic formula!