Question

A ball is launched from a sling shot. 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, it is 272 feet in the air.

Find the height, in feet, of the ball after 6 seconds in the air.

I have no idea any help?

Answer 1

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

To answer this problem, substitute 6 to x. Thus, after 6 seconds, the height is 528 feet.