Activity Overview
This activity flips factorising on its head. Two linear functions are graphed and multiplied together to produce a quadratic. The dynamic nature of the linear and quadratic graphs allow students to explore connections, ranging from axis intercepts to completing the square. Students makes sense of the instruction “express the quadratic as a product of its linear factors”.
Objectives
This activity takes into consideration the power and functionality of CAS to reframe opportunities and around student understanding about linear factors. The dynamic nature of the linear factors and the direct relationship between ‘zeros’ makes the null factor law very clear. Students also make connections between numerical factors as composite and prime and quadratic functions.
Vocabulary
- Linear Factors
- Prime / Composite
- Completing the Square
- Zeros
About the Lesson
Students start by multiplying two dynamic linear graphs together to get a quadratic. By moving the linear factors (visual), they can see the corresponding impact on the quadratic function. The x-axis intercepts align for the linear and quadratic functions. A table of values helps reinforce the null factor law. With this in mind, students are left to ponder how is it possible for a quadratic function not to touch the x-axis? Just like whole numbers occur as composite and prime, so too quadratic equations.