In this lesson, students experiment with the graphs of quadratic functions expressed in standard form and reason about how the parameters of the expressions—specifically the coefficient of the squared term and the constant term—relate to features of the graphs. Students use technology to change these values and produce the graphs. They study the effects and generalize their observations (MP8). It is enough to notice the connection between the parameters and the graphs, but an optional activity is available to explore the reason that they are connected.

Then students practice identifying equivalent quadratic expressions in standard and factored form and their corresponding graph. To do so, they look for and make use of structure (MP7). The work here strengthens students’ understanding of the ties across various representations of quadratic functions.

Note that when students graphed equations in factored form earlier, they dealt mostly with monic quadratic expressions, in which the coefficient in is 1, and the factored expression is in the form of . Limiting the examples to such expressions enables students to see more easily the connections between the numbers in the factors and the -intercepts of the graphs. When graphing from the standard form, that limitation is not necessary, as the connections between the coefficient and the features of the graph can be studied and revealed more straightforwardly.