Algebra 2 Online!
Henrico County Public Schools, Virginia
Expressions and Operations

Equations and Inequalities



SOL Review Materials
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 x-axis 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
  1. SOL A.4cf - c) solve quad equations (algebraically/graphically); f) solve real‐world problems involving equations and systems of equations
Instructional Materials
  1. VDOE ESS Lesson: Quadratic Equations - Equations and Inequalities (PDF) - Solving quadratic equations over the set of complex numbers (Word)
  2. Notes: Extracting Roots (ppt)
  3. Flowchart: Solving a Quadratic Equation (doc)
  4. Notes: Quadratic Formula (ppt)
  5. Activity: Quadratic Formula (zip)
  6. Notes: Solve by Factoring (ppt)
Real World Lessons
  1. VDOE ESS: Different Methods of Solving Quadratics Worksheet (pdf)
  2. VDOE ESS: Solving Quadratics Worksheet (pdf)
  3. VDOE ESS: Creating Quadratic Equations Worksheet (pdf)
  4. Worksheet: Extracting Roots Practice (doc)
  5. Worksheet: Quadratic Formula Practice (doc)
  6. Worksheet: Solve by Factoring Practice (doc)
  1. SOL Mini-Quiz: AII.4b - Solving Quadratic Equations
  1. JMU Pivotal Question: Quadratic Equations (doc)
  1. PH Solving Quadratic Equations by Factoring
  2. Video Tutor - Solve Quadratics by Factoring
  3. Video Tutor - Solving Quadratics by Completing the Square
  4. Video Tutor - Discriminant
  5. Video Notes: Solving Quadratics by Factoring
Explore Learning
  1. Modeling and Solving Two-Step Equations - Solve a two‑step equation using a cup‑and‑counter model. Use step‑by‑step feedback to diagnose and correct incorrect steps.
  2. Solving Two-Step Equations - Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps.
  1. Interactive Notes: Solving Quadratic Equations - lessons and practice problems from
  2. Interactive: Solving Quadratic Equations Self-Test - notes and twelve practice problems at
Common Core Standards