Question

can anyone tell me if the answer is 1292 to this problem?

A rock is launched from the cannon. After 1 second, the rock is 186 feet in the air. After 2 seconds, the rock is 344 feet in the air. Using quadratic functions, find the height, in feet, of the rock after 8 seconds in the air.

Answer 1

If we let f(t) = at^2+bt+c = 0 and we assume that c = 0 because the cannon fires from the ground then f(1) = a(1)^2+b(1)+0 = 186 and f(2) = a(2)^2+b(2)+0 = 344. Solving for a and b therefore yields a=-14 and b=200 so that f(8) = -14(8)^2+200(8)+0=708. Hence, the rocket is 704 feet high at t = 8 seconds. Does this make any sense to you?