Algebra 1 Online!
Henrico County Public Schools, Virginia
Expressions and Operations

Equations and Inequalities



SOL Review Materials
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 real-world 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 x-intercepts 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 real-world situations.
  • Set builder notation may be used to represent solution sets of equations.
Vertical Articulation
  1. SOL 7.14 - a) solve one- and two-step linear equations; b) solve practical problems in one variable
  2. 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
  3. 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
  1. 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)
  2. Notes: Quadratics (ppt)
Real World Lessons
  1. Mathalicious: Canalysis - Is there a "best" shape for cans, and if so, why aren't all cans shaped the same?
  1. VDOE ESS: Factoring for Zeros Worksheet (pdf)
  2. Worksheet: Quadratics CW (doc)
  3. Worksheet: Quadratics CW #2 (doc)
  4. Worksheet: Quadratics HW (doc)
  5. ExamView Quiz: Solving Quadratic Equations
  6. Prentice Hall Quiz
  1. JMU Pivotal Question: Quadratic Graph (doc)
  1. Video: PH Solving Quadratic Equations by Factoring
Explore Learning
  1. Solving Formulas for any Variable - Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps.
  2. 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.
  1. Interactive Notes: Solving Quadratic Equations - lessons and practice problems from
  2. Interactive: Solving Quadratic Equations Self-Test - notes and twelve practice problems at
Old Website Links
Common Core Standards