Lesson 11

Graphing from the Factored Form

Lesson Narrative

In an earlier lesson, students noticed a connection between the numbers in a quadratic expression in factored form (for example, the “2” and “8” in \((x+2)(x-8)\)) and the \(x\)-intercepts of the graph. In this lesson, they explore that connection further.

Prior to this point, students have not looked closely at how the addition and subtraction symbols in the factors affect the \(x\)-intercepts. They also have not considered how or why the connection works, or whether it is a reliable way to determine the \(x\)-intercepts. In this lesson, they verify their observations by evaluating the expressions at certain \(x\) values and seeing if they produce an output of 0.

Students also explore what the factored form can tell us about the vertex and the \(y\)-intercept of a graph representing a quadratic function.

Learning Goals

Teacher Facing

  • Create graphs of quadratic functions that are in factored form.
  • Given a quadratic function in factored form, explain how to determine the vertex and $y$-intercept of its graph.

Student Facing

  • Let’s graph some quadratic functions in factored form.

Required Preparation

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.)

The digital version of the activity “What Do We Need to Sketch a Graph?” has an applet in the launch to display for all to see. 

Colored pencils are optional for the activity “Comparing Two Graphs.”

Learning Targets

Student Facing

  • I can graph a quadratic function given in factored form.
  • I know how to find the vertex and $y$-intercept of the graph of a quadratic function in factored form without graphing it first.

CCSS Standards