In this lesson, students continue their exploration of situations polynomial functions can model. Students make connections between equivalent expressions for a polynomial function, the function’s graph, and the situation it models.
Students first consider how polynomials let us look at something familiar in a new way by identifying parallel structures between the base-10 number system and polynomials (MP7). Students will draw on these parallel structures to better understand polynomial division in later lessons. This activity also gives students an opportunity to practice evaluating polynomials for different inputs; these calculations can be tricky because polynomials have many parts, and careful attention is needed when entering expressions into a calculator. Students then examine a financial context, building a polynomial to model a simple investment account. Students may choose to use a table, equation, graph, or combination of these to make sense of and reason about this situation (MP5). Investment accounts will be revisited at the end of the unit when students calculate the sum of a finite geometric series.
- Create a polynomial to model a simple investment situation.
- Generalize the structure of integers in order to see similarities to polynomials.
- Let’s look at some other things that polynomials can model.
Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device. (Desmos is available under Math Tools.)
- I can use polynomials to understand different kinds of situations.
A polynomial function of \(x\) is a function given by a sum of terms, each of which is a constant times a whole number power of \(x\). The word polynomial is used to refer both to the function and to the expression defining it.