CCSS.Math.Content.HSA-APR.B.3
The standard
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
Common Core State Standards for Mathematics
What this standard means
Students need to connect factored form to x-intercepts. They should set each factor equal to zero, find the zeros, and use those points to sketch the general shape of the polynomial graph. They also need to notice repeated factors and how they affect the graph at an intercept.
Mastery looks like a student reading a factored polynomial, naming zeros, marking them correctly, and sketching a graph with reasonable end behavior. Common trouble spots are sign errors, forgetting multiplicity, treating every intercept as a crossing, and making a graph that ignores the degree or leading coefficient.
Ways to teach it
- Hands-on activity: Give students factor cards and graph cards, then have them match each polynomial to its zeros and rough sketch.
- Discussion or writing prompt: Ask, “How does the graph behave at x equals 2 in (x minus 2) squared?”
- Quick assessment: Put three factored polynomials on the board and have students list zeros, multiplicities, and crossing or touching behavior.
- Real-world connection: Model profit as a factored polynomial and ask where the business breaks even, then sketch the profit trend.
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Related standards
- CCSS.Math.Content.HSA-APR.B
Understand the relationship between zeros and factors of polynomials
- CCSS.Math.Content.HSF-IF.C.8a
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in ...
- CCSS.Math.Content.HSF-IF.C.7c
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
- CCSS.Math.Content.HSF-IF.C.7d
(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.