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M3-025-A09-V04
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F-IF.7.c
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M3-025-A09-V04
Graph polynomial functions using zeros, factorizations, and end behavior.
Estimate and classify polynomial turning points
Problem
A polynomial graph falls to a valley near \((1,~-5)\) and rises afterward. State the turning-point count and classification, describe the direction change, and give the minimum degree required.
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A
Count/order: 2 turns—a minimum near (1,−5), then an unspecified maximum. Trend: decreasing→increasing→decreasing. Degree bound: at least degree 3 is required for 2 turns.
B
Count/order: 0 turns. Trend: decreasing throughout with no reversal. Degree bound: a degree-1 graph cannot turn.
C
Count/order: 1 turn—a minimum near (1,−5). Trend: decreasing→increasing. Degree bound: at least degree 2 is required for a turn.
D
Count/order: 1 turn—a maximum near (1,−5). Trend: increasing→decreasing. Degree bound: at least degree 2 is required for a turn.
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Curriculum context
Standard F-IF.7.c
Category Functions
Domain Interpreting Functions
Objective Graph polynomial functions using zeros, factorizations, and end behavior.
Problem type Estimate and classify polynomial turning points
