Sketch y=(x+1)2(x-2) and y=|(x+1)2(x-2)| on separate axes. Label all axis intersections, indicate cr

Question

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

Accepted Answer

Horizontal intercepts $(-1,0)$, $(2,0)$; vertical intercept $(0,-2)$. Touches at $-1$, crosses at $2$; negative for $x<2$, except the zero at $-1$. Reflect exactly these negative portions. Modulus vertical intercept $(0,2)$. Every zero is a touching point of the modulus graph.

A factored cubic and its modulus

A factored cubic and its modulus

Solution:

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