Sketch y=(2x+1)(x-1)(x-3) and its output-modulus graph on separate axes. Label all axis intersection

Question

Sketch y=(2x+1)(x-1)(x-3) and its output-modulus graph on separate axes. Label all axis intersections, indicate crossing or touching, and state which portions reflect.

Accepted Answer

Intercepts $\left(-\dfrac{1}{2},0\right)$, $(1,0)$, $(3,0)$ and $(0,3)$. Cross at all three simple roots; the original graph is negative for $x<-\dfrac{1}{2}$ and $1<x<3$. Reflect those negative portions; modulus vertical intercept $(0,3)$. Every zero is a touching point of the modulus graph.

Interpreting cubic factors and signs

Interpreting cubic factors and signs

Solution:

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