Which statement describes the graph of f of x is equal to negative 4 x cubed minus 28 x squared minus 32 x plus 64 ?

Factor the polynomial: f(x) = -4(x - 1)(x + 4)^2. The root x = -4 has multiplicity 2, so the graph touches the x-axis there; the root x = 1 has multiplicity 1, so the graph crosses the x-axis there. This matches choice C: it touches at x = -4 and crosses at x = 1.

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