This lesson is optional because it goes beyond the depth of understanding required to address the standards. In this lesson, students examine the effects of coefficient of the linear term in standard form, the in , and how changes to it affect the graph. Students are not expected to know how to modify given expressions to transform the graphs in certain ways, but they will notice that adding a linear term to the squared term translates the graph in both horizontal and vertical directions. This understanding will help students to conclude that writing an expression such as in factored form can help us reason about the graph.

Students also practice writing expressions that produce particular graphs. To do so, students make use of the structure in quadratic expressions (MP7) and what they learned about the connections between expressions and graphs.