Today's review activity will help students solidify important ideas about the short-run and long-run behavior of polynomials, including zeros, intercepts, and end-behavior. Students switch between graphical and analytical representations of polynomials throughout the activity.
In the Graphing Polynomials task, students will be given information about a polynomial in different representations and must identify key information including the degree, leading coefficient, end-behavior, y-intercept, and zeros. Students will also sketch a polynomial given its equation and write a polynomial in intercept form when given a graph.
We suggest having students complete question 1 in small groups, debriefing as a class, and then having students complete question 2 individually. Note that question 2 features a pair of imaginary zeros. Students may struggle to draw the graph but the important piece is that students draw only one x-intercept and have the correct end behavior and a few key points.
We then have students work in small groups on question 3, where now the graph of the polynomial function is given, instead of the equation. Question 4 can be done individually in class or assigned as homework.