Grades 9/10/11 Quadratic Relations

In this lesson, students will be introduced to quadratic equations and begin to solve them by graphing, applying inverse operations, or factoring. They will also explore different methods of checking their solutions.  

In this lesson, we develop a new way to find the zeros of a quadratic relation given standard form. The Quadratic Formula will be derived and then used in a variety of contexts.

In this lesson, we recall that a quadratic relation can have either 0, 1, or 2 zeros. We develop ways to predict how many zeros the relation will have by analyzing the equation of the relation.

In this lesson, students will explore the possible number of points of intersection between a linear relation and a quadratic relation.  They will determine coordinates of the point(s) of intersection of a linear and quadratic relation both graphically and algebraically, and use the discriminant to determine how many times a linear and quadratic relation will intersect. 

In this lesson, students will solve problems involving quadratic relations relating to various applications. These problems involve both solving quadratic equations and finding a maximum or minimum, and will require the algebraic methods discussed in previous lessons. The method of partial factoring will also be introduced for determining 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.