NY Next Generation Math AII-F.IF.7.c

MathGrades 9–12Graph functions and show key features of the graph by hand and using technology when appropriate.

The Standard

Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

New York State Next Generation Mathematics Learning Standards · Analyze functions using different representations.

Teacher's field guide

What Students Need to Do: Students graph polynomial functions in Algebra II, identify zeros when useful factorizations are available, and show end behavior. They connect factors, multiplicity, and leading terms with graph features.
What Mastery Looks Like: The student plots intercepts, uses degree and leading coefficient to predict both ends, and sketches a consistent curve. Repeated zeros are represented with appropriate crossing or touching behavior.
Common Misconceptions: Students may assume every zero crosses the axis, reverse end behavior, or infer zeros from an unavailable factorization. They may draw more turns than the degree permits.
How to Assess It: Ask students to graph f(x) equals negative (x plus 2) squared times (x minus 1), labeling zeros, multiplicities, and end behavior.

Lesson moves

Use factor and leading-term cards to place zeros and end arrows before sketching a polynomial graph.
Ask students how multiplicity changes graph behavior at an x-intercept.
Play graph match with factored polynomials, zero tables, end-behavior descriptions, and sketches.
Graph a factored polynomial model for profit or volume and interpret meaningful zeros.

Keep exploring

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