A.4bcf 
The student will solve multistep linear and quadratic equations in two variables, including
b) justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets;
c) solving quadratic equations algebraically and graphically;
f) solving realworld problems involving equations.
Graphing calculators will be used both as a primary tool in solving problems and to verify algebraic solutions. 

Essential Knowledge and Skills 
 Solve equations, using the field properties of the real numbers and properties of equality, to justify simplification and solution.
 Solve quadratic equations.
 Identify the roots or zeros of a quadratic function over the real number system as the solution(s) to the quadratic equation that is formed by setting the given quadratic expression equal to zero.
 Confirm algebraic solutions to linear and quadratic equations, using a graphing calculator.

Essential Understandings 
 The process of solving quadratic equations can be modeled in a variety of ways, using concrete, pictorial, and symbolic representations.
 Properties of real numbers and properties of equality can be used to justify equation solutions and expression simplification.
 The zeros or the xintercepts of the quadratic function are the real root(s) or solution(s) of the quadratic equation that is formed by setting the given quadratic expression equal to zero.
 Equations and systems of equations can be used as mathematical models for realworld situations.
 Set builder notation may be used to represent solution sets of equations.


Vertical Articulation 
 SOL 7.14  a) solve one and twostep linear equations; b) solve practical problems in one variable
 SOL 8.15  a) solve multistep linear equations in one variable (variable on one and two sides of equations); c) ID properties of operations used to solve
 SOL AII.4  solve (algebraically/graphically) a) absolute value equation/inequalities; b) quadratic equations over complex; c) equations containing rational algebraic expression; d) equations containing radical expressions

Instructional Materials 
 VDOE ESS Lesson: Factoring for Zeros  Equations and Inequalities, Functions (PDF)  Relating the roots (zeros) of a quadratic equation and the graph of the equation (Word)
 Notes: Quadratics (ppt)

Real World Lessons 
 Mathalicious: Canalysis  Is there a "best" shape for cans, and if so, why aren't all cans shaped the same?

Practice 
 VDOE ESS: Factoring for Zeros Worksheet (pdf)
 Worksheet: Quadratics CW (doc)
 Worksheet: Quadratics CW #2 (doc)
 Worksheet: Quadratics HW (doc)
 ExamView Quiz: Solving Quadratic Equations
 Prentice Hall Quiz

SelfAssessments 

Skills 
 JMU Pivotal Question: Quadratic Graph (doc)

Videos 
 Video: PH Solving Quadratic Equations by Factoring

Explore
Learning 
 Solving Formulas for any Variable  Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps.
 Roots of a Quadratic  Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.

Websites 
 Interactive
Notes: Solving Quadratic Equations  lessons
and practice problems from Regentsprep.org
 Interactive:
Solving Quadratic Equations SelfTest 
notes and twelve practice problems at math.uww.edu

Old Website Links 

Common Core
Standards 
8.EE.7a 
8.EE.7b 
8.EE.8a 
8.EE.8b 
8.EE.8c 
ASSE.3a 
AAPR.1 
ACED.1 
ACED.2 
ACED.3 
ACED.4 
AREI.1 
AREI.3 
AREI.4a 
AREI.4b 
AREI.5 
AREI.6 
AREI.11 
FIF.8a 

