Lesson 1
1. Lesson 1
Module 3: Quadratics
Lesson 1: Investigating Quadratic Relations
Focus
Relations can be used to describe many different real-world scenarios. For example, Mathematics 10C demonstrated how linear relations can be used to describe the speed of a car. The speed of a car can be modelled by a linear relation of the form y = mx + b.
skateboard: iStockphoto/Thinkstock; dish: iStockphoto/Thinkstock; bridge: George Doyle/Stockbyte/Thinkstock
quadratic relation: a relation that can be written in standard form (y = ax2 + bx + c, where a ≠ 0); for example, 5x2 + 3x − 8
— Adapted from:
CANAVAN-MCGRATH ET AL.
Principles of Mathematics 11,
© 2012 Nelson Education Limited. p. 322.
Reproduced by permission.
Quadratic relations are another type of relation that can be used to model certain scenarios. For example, quadratic relations can be used to predict and graph the path of a skateboard in a jump. How high will the skateboard go? How far will it go? How long will it be in the air? The same is true for a thrown football, a flying hockey puck, or any projectile. Quadratic relations define the shape of satellite receivers, suspension bridge cables, and parabolic microphones.
Using quadratic relations will enable you to analyze a host of commercial and other real-world situations. Quadratic relations are useful for understanding many concepts in science, technology, business, or other fields.
Lesson Questions
This lesson will help you answer the following inquiry questions:
- How do you recognize a quadratic function?
- How do the values of a, b, and c in the standard form, y = ax2 + bx + c, affect the shape and location of the graph?
Assessment
- Lesson 1 Assignment
All assessment items you encounter need to be placed in your course folder.
Save a copy of the Lesson 1 Assignment to your course folder. You will receive more information about how to complete the assignment later in this lesson.
Materials and Equipment
- graph paper
You may find it helpful to use 1-cm Grid Paper.