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Completing the Square definitions

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  • Quadratic Equation
    An expression set equal to zero involving a variable squared, a linear term, and a constant.
  • Perfect Square Trinomial
    A three-term polynomial that can be written as a binomial squared, such as x² + 6x + 9.
  • Square Root Property
    A method allowing solutions for equations where a squared quantity equals a value, by taking square roots of both sides.
  • Binomial
    An algebraic expression with exactly two terms, often seen in squared forms like (x + 3).
  • Constant
    A fixed value in an equation or expression, not multiplied by a variable.
  • Coefficient
    A numerical factor multiplying a variable, such as the 6 in 6x.
  • Exponent
    A number indicating how many times a variable is multiplied by itself, as in x².
  • Algebraic Manipulation
    The process of rearranging and simplifying expressions to achieve a desired form.
  • Area Model
    A visual representation using shapes to illustrate terms in a quadratic, such as squares and rectangles.
  • Middle Term
    The term in a quadratic involving the variable to the first power, often split during completing the square.
  • Solution
    A value for the variable that makes the equation true when substituted back in.
  • Equality
    A statement showing two expressions have the same value, often used to balance equations.
  • Difference
    The result of subtracting one value from another, used to adjust constants when completing the square.
  • Form
    The specific arrangement or structure of an equation, such as standard or completed square.
  • Practice Problem
    An exercise designed to reinforce understanding and application of completing the square.