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Intro to Quadratic Equations definitions

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  • Quadratic Equation
    A polynomial expression where the highest exponent of the variable is 2, often written in the form ax^2 + bx + c = 0.
  • Standard Form
    An arrangement of a quadratic equation as ax^2 + bx + c = 0, with all terms on one side in descending order of exponents.
  • Coefficient
    A numerical factor multiplying a variable in an algebraic term, such as 'a' in ax^2 or 'b' in bx.
  • Constant Term
    A value in an equation that does not contain a variable, represented as 'c' in ax^2 + bx + c = 0.
  • Degree
    The highest power of the variable in a polynomial; for quadratics, this value is 2.
  • Leading Coefficient
    The coefficient of the term with the highest degree in a polynomial, specifically 'a' in a quadratic equation.
  • Factoring
    A method of rewriting a quadratic equation as a product of two binomials, which can then be set to zero to solve for the variable.
  • AC Method
    A factoring technique involving the product of 'a' and 'c' to find two numbers that multiply to ac and add to b.
  • Binomial
    An algebraic expression containing exactly two terms, such as (x + 3) or (x - 2).
  • Solution
    A value for the variable that, when substituted into the equation, makes the equation true.
  • Linear Equation
    An equation where the highest power of the variable is 1, resulting in a straight-line graph.
  • Descending Order
    An arrangement of terms in an equation from highest to lowest exponent.
  • Zero Product Property
    A rule stating that if a product of factors equals zero, at least one of the factors must be zero.
  • Second Degree Polynomial
    Another name for a quadratic equation, indicating the highest exponent of the variable is 2.
  • Verification
    The process of substituting solutions back into the original equation to confirm their validity.