Most Intersections with a Cubic

★ 6/10functions Absolute Value analytic geometry Casework

Problem

Among the following curves, determine which one has the greatest number of intersection points with the curve $y=x^3-3x$ :

y=-2x,\qquad |x|+|y|=2,\qquad y^2=4,\qquad |y|=x^2.

Justify your answer.

Answer

Solution

Difficulty	6/10
Topics	functions, Absolute Value, analytic geometry, Casework

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