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A factored cubic and its modulus

A factored cubic and its modulus

6 marks
TGM Original
Sketch y=-(x+1)(x-2)(x-4) and y=|-(x+1)(x-2)(x-4)| on separate axes. Label all axis intersections, indicate crossing or touching at each zero, and state which portions reflect.

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Answer:Horizontal intercepts \((-1,0)\), \((2,0)\), \((4,0)\); vertical intercept \((0,-8)\). Crosses at all three simple roots; negative for \(-1<x<2\) and \(x>4\). Reflect exactly these negative portions. Modulus vertical intercept \((0,8)\). Every zero is a touching point of the modulus graph.

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