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Quadratic Equations & Applications definitions

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  • Quadratic Equation
    An expression in the form ax² + bx + c = 0, used to model scenarios like projectile paths and business analysis.
  • Standard Form
    A way of writing equations where all terms are on one side and ordered by decreasing exponents, set equal to zero.
  • Trinomial
    A polynomial with exactly three terms, often seen in quadratic equations before factoring.
  • Binomial
    An algebraic expression with two terms, typically resulting from factoring a quadratic.
  • Zero Product Property
    A rule stating that if a product of factors equals zero, at least one factor must be zero.
  • Coefficient
    A numerical factor multiplying a variable in an algebraic term, such as the 'a' or 'b' in ax² + bx + c.
  • Exponent
    A number indicating how many times a variable is multiplied by itself, as in the squared term of a quadratic.
  • Factoring
    A process of rewriting a polynomial as a product of simpler expressions, often used to solve quadratics.
  • Solution
    A value for the variable that makes the equation true, often found by setting factors to zero.
  • Polynomial
    An algebraic expression made up of terms with variables raised to whole number exponents and coefficients.
  • Monomial
    A single term algebraic expression, such as 3x or -4.
  • Area
    A measure of surface, often calculated as length times width in rectangular problems involving quadratics.
  • Variable
    A symbol representing an unknown quantity, commonly solved for in equations.
  • Trial and Error Method
    A strategy for factoring by testing pairs of numbers that multiply to one value and add to another.
  • Application Problem
    A real-world scenario translated into an equation, requiring algebraic methods for solution.