A parabola passing through critical points of a curve!

Calculus Level 5

Let f(x)=x66x2+6x7 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 ya=bx2+cx+d. y^a = bx^2+cx+d. Find a+b+c+d. \mid a+b+c+d \mid .

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

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