Question

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

the general form of quadratic function is f(x)=ax^2 +bx + c
suppose x is the time (in second)
at x = 0, the height is 0 feet ->f(0) = c = 0
at x = 1 -> f(1) = a+b = 186
at x = 2 -> f(2) =4a+2b=344
solve both equations, you'll get a = -14 and b=200
so the quadratic function is f(x) = -14x^2 + 200x
then plug x=8 -> f(8) = -14(64) + 200(8) = -896 + 1600 = 704