A parabola passing through critical points of a curve!

Calculus Level 5

Let \( f(x)=x^6-6x^2+6x-7 \). It is known that this polynomial has three critical points. The equation of the parabola that passes through these three critical points is \( y^a = bx^2+cx+d.\) Find \( \mid a+b+c+d \mid .\)

Note : Critical points are defined as points where tangent is parallel to \( x \) axis.

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