# 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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