 Secondary Mathematics II

Strand: ALGEBRA - Reasoning With Equations and Inequalities (A.REI)

Solve equations and inequalities in one variable (Standard A.REI.4). Solve systems of equations. Extend the work of systems to include solving systems consisting of one linear and one nonlinear equation (Standard A.REI.7).

Standard A.REI.4

Solve quadratic equations in one variable.

• ALGEBRA - Reasoning With Equations and Inequalities (A.REI) - Sec Math II Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics II - Reasoning with Equations and Inequalities (A.REI)
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Applications of Quadratic Functions video
This video introduces and explains the topic.
• Braking Distance
The purpose of this task is to give an application arising from a real-world situation in which a quadratic equation arises, and where it is natural to use a graphical method to find an approximate solution and the quadratic formula to find an exact solution
• Completing the square
The goal of this task is to solve quadratic equations with complex roots by completing the square. Students could of course directly use the quadratic formula, but going through the process of completing the square helps reinforce the mathematics behind the quadratic formula.
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
This video introduces and explains the topic.
• Introduction to the Materials (Math 2)
Introduction to the Materials in the Mathematics Two of the The MVP classroom experience begins by confronting students with an engaging task and then invites them to grapple with solving it. As students ideas emerge, take form, and are shared, the teacher orchestrates the student discussions and explorations towards a focused mathematical goal. As conjectures are made and explored, they evolve into mathematical concepts that the community of learners begins to embrace as effective strategies for analyzing and solving problems.
• Module 3: Solving Quadratics & Other Equations - Student Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 3, Solving Quadratics & Other Equations. The idea that different quadratic forms are useful in graphing is extended in Module 3, Solving Quadratic and Other Equations, when students use different forms of quadratic equations to find the roots or solve quadratic equations of a single variable.
• Module 3: Solving Quadratics & Other Equations - Teacher Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 3, Solving Quadratics & Other Equations. The idea that different quadratic forms are useful in graphing is extended in Module 3, Solving Quadratic and Other Equations, when students use different forms of quadratic equations to find the roots or solve quadratic equations of a single variable.
• Proof Without Words: Completing the Square
The act of "completing the square" involves taking half the coefficient of x in the quadratic x2 + ax and adding its square. But many students do not understand why this process works.
This task belongs to a series of three tasks that presents students with a sequence of tile figures with the property that the n-th figure in the sequence has f(n) tiles, for some quadratic function f.
This task belongs to a series of three tasks that has students process a sequence of tile figures with the property that the n-th figure in the sequence has f(n) tiles, for some quadratic function f.
• Solve Quadratic Expressions by Factoring video
This video introduces and explains the concept.
• Solving Quadratic Equations by Completing the Square
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Solving Quadratic Equations by Factoring
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
This video introduces and explains the topic.
• Solving Quadratic Equations: Cutting Corners
This lesson unit is intended to help educators assess how well students are able to solve quadratics in one variable.
• Solving Quadratic Functions by Completing the Square video
This video introduces and explains the topic.
• Sorting Equations and Identities
This lesson unit is intended to help educators assess how well students are able to recognize the differences between equations and identities, as well as substitute numbers into algebraic statements in order to test their validity in special cases.
• Springboard Dive
The problem presents a context where a quadratic function arises. Careful analysis, including graphing, of the function is closely related to the context. The student will gain valuable experience applying the quadratic formula and the exercise also gives a possible implementation of completing the square.
• Systems of Non-Linear Equations
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Systems of Non-Linear Equations video
This video introduces and explains the topic.
• Two Squares are Equal
This classroom task is meant to elicit a variety of different methods of solving a quadratic equation.
• Vertex of a parabola with complex roots
The goal of this Illustrative Mathematics task is to study the relationship between the roots of a quadratic function and its graph.
• Visualizing Completing the Square
The purpose of this task is to help provide geometric intuition for the algebraic process called ''completing the square.'' http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Joleigh Honey and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer Throndsen .

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.