Introduction
For this lesson, we will put everything that we learned in this unit to graph polynomials.
We will use what we learned about finding solutions and end behavior, and combine it with learning how to estimate maximum and minimum points to sketch a graph of a polynomial.
Following successful completion of this lesson, students will be able to...
- Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
- 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.
Essential Questions
- How does the factorization of a polynomial reveal a root of that polynomial?
- How does a rearrangement of the terms of a polynomial expression reveal a recognizable factorable form of the polynomial?
- What are the relationships of roots to points on the graph of the polynomial?
Enduring Understandings
- Students understand how to solve a variety of functions, and the effects of transformations on functions to describe an object.
The above objectives correspond with the Alabama Course of Study: Algebra II with Statistics standards: 6, 17, 20, and 20a.