Following toggle tip provides clarification
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
Unit 4: Graphing Quadratic Relations
In this lesson, transformations will be explored. We will consider translations, reflections in the \(x\)-axis, and vertical stretches of parabolas. We will look at the relationship between these transformations and the equation of a parabola.
This lesson discusses the relationship between the graph of a quadratic relation and its equation in vertex form. Methods of generating the graph of a relation from its equation, including the application of transformations, will be explored, as well as how to identify the equation of a relation from its graph.
In this lesson, a brief recap of factored form is given. We then extend our understanding of factored form to graph the quadratic relation.
This lesson will discuss methods of sketching the graph of a quadratic relation whose equation is given in standard form, \(y=ax^2+bx+c\). These methods include writing the equation in vertex form first by completing the square, or factoring the equation if possible to find the zeros.
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.