Properties of Real #s Quadratic Equations Factoring Commutative To solve: Look for GCF first!! Associative Factor: set equation to 0; factor; set each factor to 0; check GCF: Difference Of Perfect Quadratic Formula: Squares: Distributive Identity Completing the Square Trinomial: Inverse Zero Square Root Property If , then Polynomials Add combine like Variation – Subtract add the opposite Direct Variation x & y increase/decrease – – Multiply- distribute together Inverse Variation as x increases, y decreases – Solving Equations Divide divide each term – Distribute to get rid of parentheses. Real Number System Combine like terms on the same side of the =. Exponents Get all variables on one side and the constants on the other. Divide or multiply to solve. Inequalities Solve like an equation. Graph on a # line (open circle <,>; closed circle ) Test critical points or put in calc. State Solution with and /or. ** reverse inequality when multiplying or dividing by a negative value Absolute Value Equations Interval Notation (1,5] Pythagorean Theorem Use ( ) for < or >; [ ] for To find a missing side of a right triangle: Where c is the hypotenuse Solve System of Equations Degree Substitution solve one of the equation for x or y and sub into the other. Monomial sum of exponents – – Elimination/Addition create opposites by mult equation and add equations Polynomial highest exponent – –
Properties of Real #s Commutative Associative Distributive Identity Inverse Zero Square Root Property If , then Quadratic Equations To solve: Factor: set equation to 0; factor; set each factor to 0; check Quadratic Formula: Completing the Square Factoring Look for GCF first!! GCF: Difference Of Perfect Squares: Trinomial: Polynomials Add – combine like Subtract – add the opposite Multiply- distribute Divide – divide each term Variation Direct Variation – x & y increase/decrease together Inverse Variation – as x increases, y decreases Solving Equations Distribute to get rid of parentheses. Combine like terms on the same side of the =. Get all variables on one side and the constants on the other. Divide or multiply to solve. Inequalities Solve like an equation. Graph on a # line (open circle <,>; closed circle ) Test critical points or put in calc. State Solution with and /or. ** reverse inequality when multiplying or dividing by a negative value Real Number System Exponents Absolute Value Equations Interval Notation (1,5] Use ( ) for < or >; [ ] for Pythagorean Theorem To find a missing side of a right triangle: Where c is the hypotenuse Solve System of Equations Substitution – solve one of the equation for x or y and sub into the other. Elimination/Addition – create opposites by mult equation and add equations Degree Monomial – sum of exponents Polynomial – highest exponent
Algebra%201%20CC%20Study%20Guide.docx