Florida B.E.S.T. MA.912.AR.6.5
The Standard
Sketch a rough graph of a polynomial function of degree 3 or higher using zeros, multiplicity and knowledge of end behavior.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use the degree and leading coefficient to predict the left and right tail directions. They locate zeros, use multiplicity to show crossings or touches, and connect the features with a smooth curve.
What Mastery Looks Like
- Given a factored polynomial, the student correctly marks each zero and shows whether the graph crosses or touches the x-axis. Both tails match the degree and leading coefficient. The student can explain each feature using the factors.
Common Misconceptions
- Students may graph a zero at 2 for a factor of (x + 2), or treat every zero as a crossing. They may ignore the leading coefficient when choosing tail directions. Some draw sharp corners or add zeros not shown by the factors.
How to Assess It
- On an exit ticket, have students sketch f(x) = -(x + 2)^2(x - 1)^3 and label each zero, multiplicity, crossing or touch, and tail direction.
Lesson moves
Ways to Teach It
Place zero and multiplicity cards on a floor number line, then use yarn to build a curve with the required crossings and turns.
Show two sketches with the same zeros and ask students which matches the given multiplicities and leading coefficient, then defend their choice.
Run a card sort matching factored equations, end behavior descriptions, zero tables, and rough graphs.
Use a polynomial roller coaster profile and ask how repeated zeros make the track touch ground level without crossing it.
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Related Standards
- MA.912.AR.6.4
Given a table, equation or written description of a polynomial function of degree 3 or higher, graph that function and determine its key features.
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- MA.912.AR.6.6
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