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Completing the Square definitions

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  • Quadratic Equation
    An expression involving a variable squared, a linear term, and a constant, often solved for variable values.
  • Perfect Square Trinomial
    A three-term polynomial formed by squaring a binomial, resulting in a specific quadratic structure.
  • Square Root Property
    A principle allowing solutions of equations where a squared quantity equals a constant by taking square roots.
  • Binomial
    An algebraic expression consisting of two terms, often used in forming squared expressions.
  • Constant Term
    A value in a polynomial that does not contain any variables and affects the equation's balance.
  • Coefficient
    A numerical factor multiplying a variable in a polynomial, crucial for splitting terms during the process.
  • Standard Form
    A way of writing a quadratic equation as ax² + bx + c, organizing terms by degree.
  • Area Model
    A visual representation using squares and rectangles to illustrate polynomial terms and their relationships.
  • Side Length
    A measure used in the area model to represent variable and constant values in geometric diagrams.
  • Difference
    The value needed to adjust constant terms when transforming a quadratic into a perfect square trinomial.
  • Solution
    A value for the variable that satisfies the quadratic equation, often found after completing the square.
  • Equality
    A balanced equation showing two expressions are equivalent, essential for solving quadratics.
  • Rectangle
    A geometric shape used in the area model to represent linear terms split during the process.
  • Practice Problems
    Exercises designed to reinforce understanding and application of completing the square.
  • Check
    A step involving substituting solutions back into the original equation to verify correctness.