Quadratic functions are relationships between two variables that have a constant second rate of change (the rate of change changes at a constant rate).
Activity
Begin by working through the Triangular Number Problem. Download the document and either mark it up on your screen with your finger or a touch-pen or print it and use a pencil. Please pay particular attention to the number patterns in the table .
1.6_-Algebraic-Reasoning-SWTDownload the Triangular Number Problem.
Reflect
On your own paper or digital document (or in your professional learning log!), answer these two questions.
- In a linear function, the first finite differences are constant. What is true about the finite differences for a quadratic function?
- A linear function contains a polynomial with degree one (mx + b) and a quadratic function contains a polynomial with degree two (ax^2 + bx + c). What relationship is there between the degree of the polynomial and the level of finite differences that are constant?
Why does that work?
Next, watch the video to see how finite differences relate to quadratic functions.
Connections and Teaching Hints
Here’s a video showing connections to Algebra 1 as well as other hints for teaching this topic with your kids from the author’s perspective.
