The purpose of this lesson is for students to bring together what they have learned so far about sketching graphs of polynomials expressed in factored form and factoring polynomials using division. The main activity is an Information Gap in which students must ask for the information they need to factor a polynomial and then sketch its graph, requiring them to use precise language as they work with their partner (MP6).
- Determine what information is needed to sketch a polynomial function given a known factor. Ask questions to elicit that information.
- Let's put together what we've learned about polynomials so far.
- I can use division to rewrite a polynomial in factored form starting from a known factor and then sketch what it looks like.
How the outputs of a function change as we look at input values further and further from 0.
This function shows different end behavior in the positive and negative directions. In the positive direction the values get larger and larger. In the negative direction the values get closer and closer to -3.
The power to which a factor occurs in the factored form of a polynomial. For example, in the polynomial \((x-1)^2(x+3)\), the factor \(x-1\) has multiplicity 2 and the factor \(x+3\) has multiplicity 1.