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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 of the form (expression)^2 = constant by taking both positive and negative roots.
  • Constant
    A fixed value in an equation, often isolated on one side when solving quadratics.
  • Factoring
    The process of rewriting a polynomial as a product of simpler expressions, such as binomials.
  • Binomial
    An algebraic expression containing exactly two terms, such as x + 3.
  • b over 2 squared
    The value obtained by halving the coefficient of x and squaring the result, used to complete the square.
  • Solution
    A value or set of values for the variable that satisfies the given equation.
  • Isolating the Constant
    The step of rearranging an equation so that the constant term stands alone on one side.
  • Squared Expression
    A mathematical phrase where a binomial or variable is raised to the second power, such as (x + 3)^2.
  • Positive and Negative Square Roots
    The two possible values, one positive and one negative, that result from taking the square root of a number.
  • Even Coefficient
    A coefficient of x that is divisible by 2, making completing the square more straightforward.
  • Rearrangement
    The process of moving terms within an equation to achieve a desired form, such as x^2 + bx = c.
  • Factored Form
    An expression written as a product of its factors, such as (x + 3)^2.