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Completing the Square definitions Flashcards

Completing the Square definitions
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  • Quadratic Equation
    An algebraic expression set to zero, featuring a variable raised to the second power as its highest degree.
  • Leading Coefficient
    The numerical factor in front of the highest degree term in a polynomial, often denoted as 'a' in ax^2 + bx + c.
  • Perfect Square Trinomial
    A three-term polynomial that factors into the square of a binomial, such as x^2 + 6x + 9.
  • Square Root Property
    A method for solving equations where a squared expression equals a constant, allowing extraction of both positive and negative roots.
  • Binomial
    An algebraic expression consisting of exactly two terms, such as x + 3.
  • Constant
    A fixed value in an equation, often represented as 'c', that does not contain variables.
  • Factoring
    The process of rewriting a polynomial as a product of simpler expressions, often used to simplify solving equations.
  • b over 2 squared
    A value calculated by halving the linear coefficient and squaring the result, crucial for forming a perfect square trinomial.
  • Isolated Squared Expression
    A squared term positioned alone on one side of an equation, ready for the application of the square root property.
  • Solution Set
    The collection of all possible values for the variable that satisfy the given equation.
  • Even Coefficient
    A linear term's numerical factor that is divisible by two, making certain algebraic methods more convenient.
  • Form x squared plus bx equals c
    A standard arrangement of a quadratic equation with the quadratic and linear terms on one side and the constant on the other.
  • Negative Root
    The solution obtained by taking the negative value when applying the square root property to a squared equation.
  • Positive Root
    The solution obtained by taking the positive value when applying the square root property to a squared equation.
  • Factored Form
    An expression rewritten as a product of its factors, such as (x + 3)^2, simplifying the process of finding solutions.