Lesson 14

Graphs That Represent Situations

Lesson Narrative

By now students have seen how the parameters of a quadratic expression in standard form and in factored form relate to the graph representing the function. In the past few lessons, students worked with decontextualized quadratic functions. In this lesson, they transfer what they learned about the graphs to make sense of quadratic functions that model concrete contexts.

Students interpret equations and graphs of quadratic functions in terms of the situations they represent. They use their analyses to solve problems and to compare quadratic functions given in different representations. Along the way, they practice reasoning quantitatively and abstractly (MP2).

Learning Goals

Teacher Facing

  • Interpret (orally and in writing) the graph and equation representing a function in terms of the context.

Student Facing

  • Let’s examine graphs that represent the paths of objects being launched in the air.

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.)

Learning Targets

Student Facing

  • I can explain how a quadratic equation and its graph relate to a situation.