Which statement describes the graph of f(x) = –4x3 – 28x2 – 32x + 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 and turns around. The root x = 1 has multiplicity 1, so the graph crosses the x-axis there. Therefore, the statement that it touches at x = −4 and crosses at x = 1 is correct.

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