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Grades 9/10/11 Quadratic Relations
Graphs and tables. Standard, factored, and vertex forms. Algebra of quadratic relations. Quadratic equations. Intersections of lines and parabolas.
This is one of seven strands of the CEMC Grade 9/10/11 courseware. The other strands and more information about this courseware is available on the Grade 9/10/11 homepage.
Units
Unit 1: Basic Properties of Quadratic Relations
Unit 2: Algebraic Representations of Quadratic Relations
Unit 3: Algebraic Skills
In this lesson, students will apply the distributive property to multiply and square binomials. They will practise expanding and simplifying in the context of quadratic relations, particularly changing equations from factored or vertex form to standard form.
In this lesson, students will begin learning about factoring. Factoring is the algebraic process that converts a standard form equation into a factored form equation, making it easy to find the zeros. This lesson focuses on common factoring and factoring trinomials of the form \(ax^2+bx+c\).
In this lesson, students will complete their study of factoring. This lesson focuses on difference of squares, perfect squares, and combining multiple types of factoring together.
In this lesson, students will be introduced to the process of completing the square, for the purpose of changing the equation of a quadratic relation from standard form to vertex form. They will move from more simple examples to more complex cases with fractions, and apply the process in contexts where they need to find the vertex.
All of the pencil and paper practice exercises, answers, and solutions for this unit are reproduced here.
This is a collection of additional, and sometimes challenging, problems that extend the material covered in this unit, connect material from different lessons, and further explore real-world applications.