[TEA-T2] MPM2D Princ ...

Subject:MPM2D MATHEMATICS

Grade: 10

Lesson No: 3.2

Duration: 3 hours

Unit 3 - Graphs of Quadratic Relations

Topic: 3.2- Factored Form of a Quadratic Relation

Overall Expectations (Directly from The Ontario Curriculum)

• manipulate algebraic expressions, as needed to understand quadratic relations;

• identify characteristics of quadratic relations;

• solve problems by interpreting graphs of quadratic relations

Specific Expectations (Directly from The Ontario Curriculum)

compare, through investigation using technology, the graphical representations of a quadratic relation in the form y = x2 + bx + c and the same relation in the factored form y = (x – r)(x – s) (i.e., the graphs are the same), and describe the Quadratic Relations of the Form y ax2 = + bx + c FOUNDATIONS OF MATHEMATICS, GRADE 10, APPLIED (MFM2P) 59 connections between each algebraic representation and the graph [e.g., the y-intercept is c in the form y = x2 + bx + c; the x-intercepts are r and s in the form y = (x – r)(x – s)] (Sample problem: Use a graphing calculator to compare the graphs of y = x2 + 2x – 8 and y = (x + 4)(x – 2). In what way(s) are the equations related? What information about the graph can you identify by looking at each equation? Make some conclusions from your observations, and check your conclusions with a different quadratic equation.).

Learning Goals

Today you will Investigate Factored Form of a Quadratic Relation

Success Criteria

By the end of class:

-    I can relate the factors of a quadratic relation to the key features of its graph.

Materials and Resources

-    Graphing calculator and/or graph paper

-    Laptop with Internet access

Lesson Structure and Activities

Timing

Lesson

~10 minutes

~20 minutes

~20 minutes

~60 minutes

~60 minutes

~10 minutes

1.  Students to Read Lesson Plan

2.  Students to Study Glossary

3.  Students to complete Warmer Question

4.   Students to study Lesson

5.  Students to complete Assignment

6.  Students to complete Exit card