Question

Function f is a quadratic function. The graph of y = f(x) in the xy-plane has a ver- tex at (-8, 1), contains the point (9, - 1), and has a y intercept at (0, a). The graph of y = 6. f(x) has a y intercept at (0, b). What is the positive difference between a and b?

Answer 1

Write f in vertex form: f(x) = A(x + 8)^2 + 1. Using (9, −1):
-1 = A(17)^2 + 1 => 289A = −2 => A = −2/289.

So a = f(0) = A(8)^2 + 1 = (−2/289)·64 + 1 = 161/289.
Then b = 6a = 966/289, and the positive difference is b − a = 5a = 5·161/289 = 805/289.