A factored cubic and its modulus
A factored cubic and its modulus
6 marks
TGM Original
Sketch y=(x+2)(x-1)(x-3) and y=|(x+2)(x-1)(x-3)| on separate axes. Label all axis intersections, indicate crossing or touching at each zero, and state which portions reflect.
Solution:
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Answer:Horizontal intercepts \((-2,0)\), \((1,0)\), \((3,0)\); vertical intercept \((0,6)\). Crosses at all three simple roots; negative for \(x<-2\) and \(1<x<3\). Reflect exactly these negative portions. Modulus vertical intercept \((0,6)\). Every zero is a touching point of the modulus graph.
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