Doubly Tangent Parabola
Let the quartic function \( f(x) \) be given by
\[ f(x) = x^4 - 8 x^3 +17 x^2+ 2x - 24 \]
A parabola Q(x) is tangent to the graph of \( f(x) \) at two distinct points, and in addition, passes through the point \( (2, -20) \). Let this parabola be described by
\[ Q(x) = a x^2 + b x + c \]
Find \( | a |+ | b |+ | c | \).