Representing Quadratic Functions Graphically
This lesson unit is intended to help you assess how well students are able to understand what the different algebraic forms of a quadratic function reveal about the properties of its graphical representation. In particular, the lesson will help you identify and help students who have the following difficulties:
- Understanding how the factored form of the function can identify a graph’s roots.
- Understanding how the completed square form of the function can identify a graph’s maximum or minimum point.
- Understanding how the standard form of the function can identify a graph’s intercept.
- Before the lesson, students work individually on an assessment task that is designed to reveal their current understandings and difficulties. You then review their work and create questions for students to answer in order to improve their solutions.
- After a whole-class interactive introduction, students work in pairs on a collaborative discussion task in which they match quadratic graphs to their algebraic representation. As they do this, they begin to link different algebraic forms of a quadratic function to particular properties of its graph.
- At the end of the lesson there is a whole-class discussion.
- In a follow-up lesson students attempt to improve their original response to the assessment task.
- Each individual student will need two copies of the Quadratic Functions assessment task and a mini-whiteboard, pen, and eraser.
- Each pair of students will need Domino Cards 1 and Domino Cards 2, cut into ten ‘dominoes’.
15 minutes before the lesson, a 95-minute lesson (or two shorter lessons), and 10 minutes in a follow-up lesson. Timings are approximate and will depend on the needs of the class.
This lesson involves a range of mathematical practices from the standards, with emphasis on:
- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
- MP5: Use appropriate tools strategically
- MP6: Attend to precision
- MP7: Look for and make use of structure
- MP8: Look for and express regularity in repeated reasoning
Mathematical Content Standards
This lesson asks students to select and apply mathematical content from across the grades, including the content standards:
- H.A-SSE: Write expressions in equivalent forms to solve problems
- H.F-IF: Analyze functions using different representations