Doubly Tangent Parabola

Calculus Level 5

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 \( | a |+ | b |+ | c | \).

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