a ball is launched from a slingshot. its height, h(x), can be represented by a quadratic function in terms of time, x, in seconds.

after 1 second, the ball is 148 feet in the air, after 2 seconds the ball is 272 feet in the air.

find the height in feet of the ball after 6 seconds in the air?

For the answer to the question above,

From the data given, generate first the quadratic equation which best describe the height of the ball. The quadratic function has a general form of 
f(x) = Ax^2 + Bx 

Substituting the known data,

(1)            148 = A(1^2) + B(1)
(2)             272 = A (2^2) + B (2)
solving for A and  B simultaneously, 

A = -12
B = 160
So the to answer this problem, substitute 6 to x. Thus, after 6 seconds, the height is 528 feet.