Have the class learn about and make conjectures about a line intersecting a cubic.  In this making conjectures about a line intersecting a cubic lesson, students draw lines that intersect a cubic at three different points.  Students determine the sum of the intersection points.  Students repeat the process for various cubics.  Students make a conjecture that the sum of the three x-values of the intersection points is always -a.

Concepts

cubic units, linear functions, functions, polynomials

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Additional Tags

cubic, linear functions, making conjectures, polynomials, math

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Classroom Considerations

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Common Core

HSA-APR.B.3 HSA-CED.A.2 HSF-IF.C.7.a HSF-LE.A.1.a MP4 MP5