Properties Commutative Property 3+5=5+3 3*5=5*3 (change order) Associative property (3+4) +5 = 3+ (4+5) same for multiplication (grouping) Identity Property a*1= a a+0=a (What you start with is what you end with) Distributive Property 3(a+8) = 3a+24 Multiplicative Property of Zero x*0=0 Reflexive property ab=4 ab=4 IF THEN (the same on both sides) Symmetry property xy=6 6=xy IF THEN (flipped ---Has to have the if then) Transitive x+2=y and y=6 x+2=6 If then (three items) Function Families: Linear (/ ),Quadratic (U), Absolute value (V), Rational (2 curves) , exponential , Logarithmic Polynomial Odd degree Even degree Square root Interval of Increasing or decreasing Use only the X values and look at the graph to decide where it is increasing or decreasing End behavior= What direction the graph going at the ends. f(x) ___ as x _____ +∞ -∞ Use or for the blanks or numbers for Roots, Logs, Expos Parent Functions- Horizontal if the number is changing the x Rule” “Golden Vertical shift is the number that is not with the x Absolute equations- 2bars 2 equations! Look out for bars equaling a negative number That’s a {no solution} Variations Direct Variation-Where the line goes through the Also uses y=kx, where k is the constant (slope) origin. Indirect/Inverse Variation- (division) Joint Variation- y=kxz (Needs two or more items) Polynomials Standard form ax2+bx+c=0 highest degree 1st Degree of polynomial is the largest exponent. FACTOR—Check for GCF first (could be # or variable or both) Sign rules for factoring ___ + ___ + ____ Difference of Perfect Squares x2-4 (prefect square) - (perfect square) Perfect trinomials ( + )2 signs are the same, either + or – Difference of = signs” “alternate Quadratics ax2+bx+c=0 **Must show for zero **Can factor or y= key
Properties Commutative Property 3+5=5+3 3*5=5*3 (change order) Associative property (3+4) +5 = 3+ (4+5) same for multiplication (grouping) Identity Property a*1= a a+0=a (What you start with is what you end with) Distributive Property 3(a+8) = 3a+24 Multiplicative Property of Zero x*0=0 Reflexive property IF ab=4 THEN ab=4 (the same on both sides) Symmetry property IF xy=6 THEN 6=xy (flipped ---Has to have the if then) Transitive If x+2=y and y=6 then x+2=6 (three items) Function Families: Linear (/ ),Quadratic (U), Absolute value (V), Rational (2 curves) , exponential , Logarithmic Polynomial Odd degree Even degree Square root Interval of Increasing or decreasing Use only the X values and look at the graph to decide where it is increasing or decreasing End behavior= What direction the graph going at the ends. f(x) ___ as x _____ Use +∞ or -∞ for the blanks or numbers for Roots, Logs, Expos Parent Functions- Horizontal if the number is changing the x “Golden Rule” Vertical shift is the number that is not with the x Absolute equations- 2bars 2 equations! Look out for bars equaling a negative number That’s a {no solution} Variations Direct Variation-Where the line goes through the origin. Also uses y=kx, where k is the constant (slope) Indirect/Inverse Variation- (division) Joint Variation- y=kxz (Needs two or more items) Polynomials Standard form ax2+bx+c=0 highest degree 1st Degree of polynomial is the largest exponent. FACTOR—Check for GCF first (could be # or variable or both) Sign rules for factoring ___ + ___ + ____ Difference of Perfect Squares x2-4 (prefect square) - (perfect square) Perfect trinomials ( + )2 signs are the same, either + or – Difference of = “alternate signs” Quadratics ax2+bx+c=0 **Must show for zero **Can factor or y= key
ALGEBRA-2-SOL-REFERENCE-SHEET2013.docx