Study Guide
Learning Objectives
- Identify polynomial degree, leading term, and leading coefficient.
- Describe local and global extrema using increasing/decreasing switches.
- Apply: between two distinct real zeros, at least one local extremum.
- Explain why even-degree polynomials have a global max or min (quadratic: vertex).
- Describe points of inflection via change in the rate of change / concavity.
Suggested Practice Sequence
1. Degree and leading coefficient from equations. 2. Graph reading: label local max/min; decide global if any. 3. Factored polynomials: zeros → guaranteed turns between them. 4. Even vs odd degree: global extrema existence. 5. Inflection vs extremum comparison items. 6. Mixed multi-step write-ups with 1.1/1.2 rate language.
Classroom / Check-In Moves
- Require the phrase "switches from increasing to decreasing" for local max.
- Cold-call: "Does this even-degree graph have a global max or min?"
- Show a cubic inflection with no horizontal tangent language—focus on concavity change.
Misconception Watch-List
- Local = global.
- Inflection = turning point.
- Odd degree ⇒ bounded above and below.
Vocabulary to Own
- degree, leading term, leading coefficient
- local (relative) maximum / minimum
- global (absolute) maximum / minimum
- point of inflection
- concave up / concave down
Materials Map
- Practice: identification + graph/feature claims
- Word: applied polynomial height/cost models with turns
- Mixed / multi-*: link to increasing/decreasing and AROC
- Review & practice test: timed feature recognition
- Interactive: quick MCQ/typed checks