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.
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