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GOLDEN RULE: ALGEBRA 2 SOL REFERENCE SHEET If it is in a parenthesis—DO THE OPPOSITE!!! This you need to memorize for the SOL test. 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 Distributive Property 3(a+8) = 3a+24 Multiplicative Property of Zero x*0=0 Reflexive property ab=ab (the same on both sides) Symmetry property ab=ba (flipped) Key words: sum, product, difference, twice, less than, greater than, etc. Matrices: rows by columns [2 3 5 6] would be 1x 4 When adding or subtract match the elements (same location) Scalar Multiplication is just distributive property for matrices. System of equations with matrices—[A]-1 * [B] Matrix A is the coefficients, Matrix B is the answer column FUNCTIONS!!! The x coordinates cannot be the same to be a function (2,3) (3,5) is a function. Vertical line test One x to any y Function Families: Quadratic (u), Linear (line), Absolute value (V), Rational , exponential (lazy J) f(x)= x +3 f(4) just replace x with the 4***Use parentheses around new values*** Odd degree Even degree Zero of function---what would x equal to make the function equal zero Where does the graph cross the x-axis? y2 y1 x2 x1 SLOPE!! Change of y over x RISE OVER RUN y=mx+b m equals slope and b is the y-intercept(were line crosses the y-axis) Remember positive lines go up and negative lines go down Horizontal line is a zero slope and vertical lines are undefined slopes y-axis X= is a vertical line Y= is a horizontal line x-axis Variations can be solved using proportions y y x x Direct Variation-Where the line goes through the origin. Also uses y=kx, where k is the constant (slope) Indirect Variation- y k Remember this is where you switch the x’s is the proportional setup x Joint Variation- y=kxz Systems of equations 3 types of solutions: No solution (parallel lines), ∞ solutions (same line), one solution (where lines crosseach other, it’s a coordinate) 4 ways to solve: Graph (solve for y) Substitution method, elimination method, matrices Polynomials Standard form ax2+bx+c=0 highest degree 1st Degree of polynomial is the largest exponent. Don’t forget the Martinsville method for trinomials with a leading number. FACTOR—Check for GCF first (could be # or variable) Sign rules for factoring ___ + ___ + ____ This sign is the result when you add the two factors together If you see (+) Add or (-) subtract the factors to make the middle number Difference of Perfect Squares x2-4 (prefect square) - (perfect square) Perfect trinomials ( + )2 signs are the same, either + or – Difference of cubics x3 8 = ( x 2)( x 2 4 x 4) “alternate signs” Quadratics ax2+bx+c=0 **Must show for zero **Can factor or y= key I’m a pothole The turning point is where the graph turns Maximum Opens Down a<0 Minimum Opens up a>0 If a=0 then it’s a linear equation not a parabola (u shaped) Vertex ( , ) where the min and max is located. Go to y= then graph, 2nd trace choose max or min then hit enter, enter, enter. Axis of symmetry always is x=(the first coordinate of the vertex) Asymptotes-where the graph cannot have a number is the denominator Point discontinuity (hole)-Where a binomial gets cancelled out. 1 x2 x 2 Conics—Remember if it is in a parenthesis then the answer is the opposite sign! Parabola y a( x h)2 k or x a( y k )2 h Circle x h y k r 2 2 Ellipse x h 2 2 a2 Hyperbola y k b2 x h 2 a2 x h 2 1 y k b2 2 b2 2 1 y k a2 y k 2 a2 2 x h b2 1 2 1 The following all mean the same thing—Find where the graph crosses the x-axis -Zero of the function -Factors -Real solutions -x-intercepts -Roots Scatter plots or best fit of line-go to STAT EDIT CAL 4 ENTER Rational Functions-Must have like denominators to add the numerators. Sometimes you have to factor to see the new denominator. Remember: What you see is what you need for the LCD!! Sequences and Series Arithmetic sequence an a1 (n 1)d geometric sequence an a1 r n 1 end Series (summation)- formula start Calculator format sum(seq(formula, variable, start, end, count)) ***Foreign Veggies Seem Extremely Crunchy*** sto X Storing a value for x number the x will remain the same value until you restore Remember to work out all your problems and read the questions carefully.