AII.4b 
The student will solve, algebraically and graphically,
b) quadratic equations over the set of complex numbers.
Graphing calculators will be used for solving and for confirming the algebraic solutions 

Essential Knowledge and Skills 
 Solve a quadratic equation over the set of complex numbers using an appropriate strategy.
 Calculate the discriminant of a quadratic equation to determine the number of real and complex solutions.
 Recognize that the quadratic formula can be derived by applying the completion of squares to any quadratic equation in standard form. †Revised March 2011

Essential Understandings 
 A quadratic function whose graph does not intersect the xaxis has roots with imaginary components.
 The quadratic formula can be used to solve any quadratic equation.
 The value of the discriminant of a quadratic equation can be used to describe the number of real and complex solutions.
 Equations can be solved in a variety of different ways.
 Set builder notation may be used to represent solution sets of equations and inequalities.


Vertical Articulation 
 SOL A.4cf  c) solve quad equations (algebraically/graphically); f) solve real‐world problems involving equations and systems of equations


Instructional Materials 
 VDOE ESS Lesson: Quadratic Equations  Equations and Inequalities (PDF)  Solving quadratic equations over the set of complex numbers (Word)
 Notes: Solving Equations (Mixed) by Graphing (ppt)

Real World Lessons 

Practice 
 VDOE ESS: Different Methods of Solving Quadratics Worksheet (pdf)
 VDOE ESS: Solving Quadratics Worksheet (pdf)
 VDOE ESS: Creating Quadratic Equations Worksheet (pdf)

SelfAssessments 
 SOL MiniQuiz: AII.4b  Solving Quadratic Equations

Skills 
 Mathematics Assessment Project: E05:Fearless Frames  Expert  Fearless Frames Inc makes metal frames for containers. Your task is to find the maximum volume of prismshaped frame that can be made with a limited supply of metal.
 JMU Pivotal Question: Quadratic Equations (doc)

Videos 

Explore
Learning 
 Modeling and Solving TwoStep Equations  Solve a two‑step equation using a cup‑and‑counter model. Use step‑by‑step feedback to diagnose and correct incorrect steps.
 Solving TwoStep Equations  Choose the correct steps to solve a twostep equation. Use the feedback to diagnose incorrect steps.

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

Common Core
Standards 
NCN.7 
NCN.8 
AREI.2 
AREI.4a 
AREI.4b 
FIF.7b 
FIF.8a 
