Algebra 2 Things to MEMORIZE

Algebra 2 – Things to MEMORIZE Properties 1. Commutative – move 3a + 4 = 4 + 3a 5(3x) = (3x)5 2. Associative – parenthesis change (2a + 3) + 5 = 2a + (3 + 5) 5(3a)  (53)a 3. Identity – get same value by + or * 3a + 1 + 0 = 3a + 1 2a(1) = 2a 1 4. Inverse – flip sign or number 3a – 3a = 0 5   1 5 5. Reflexive – mirror 3x + 2 = 3x + 2 3x(2a) = 3x(2a) 6. Distributive – teacher 5(a + 4) = 5a + 5(4) 7. Symmetric – If, then 2 = If 3 = 5a then 5a = 3 8. Transitive – If, then 3 = If 4 = 2a and 2a = 5p, then 4 = 5p

Types of Functions Linear – Line - Equation has degree of 1 Quadratic – U – parabola--Equation has a degree of 2 Absolute Value – V – Equation has bars Cube (or cubic) – wiggle – Equation has an exponent of 3 Exponential – – Equation has exponent of x—horiz. Asymptote y = 0  changes when graph moves up/down Logarithmic – --Equation has LOG or LN -- vertical asymptote x = 0changes when graph moves right/left Rational – curves with vert. asymptote (set denominator = 0) & horiz. asymptote (y = 0 or top coeff/bottom coeff)– Equation is a fraction Square Root (Radical) – curve with definite start (1/2 of sideways parabola) – Equation has a square root symbol Cube Root – sideways cube graph - Equation uses cube root symbol

Roots and Zeros Degree = total solutions! Roots, zeros, solutions, x intercepts are the SAME Factors are (x minus the above) Ex. If root is -5factor is (x + 5), if root is 7factor is (x – 7) Double root—‘bounces’ off x-axiscounts 2x Single root- ‘crosses through’ x-axiscounts 1x Triple root--- ‘wiggles’ through x-axiscounts 3x

Direct, Inverse and Joint Variation Direct is multiply: y=kx Inverse is divide: y = k/x Joint is multiply with 2 variables joined together: y = kxz Combined- direct and inverse: y = (kx)/(z)

Arithmetic or Geometric Arithmetic – add same value Geometric – multiply same value

Solutions from Graphs One Graph – Answers are where the graph touches the x axis. More than one Graph – Solutions are where the graphs touch each other.

Line or Curve of Best fit Stat Edit Y = Plot 1 Zoom 9 (to see dots on graph) Line – Stat Calc #4 LINREG(ax+b) Parabola – Stat Calc #5 QUADREG Exponential – Stat Calc #0 EXPREG Logarithm – Stat Calc #9 LNREG

Normal Curve Area under the curve is 100% OR 1. 68% within 1 standard deviation 95% within 2 standard deviations 99.7% within 3 standard deviations Looking up Z-score value from formula ---table shows % < than value --- (1.0 – table value) gives % > than value

Permutations and Combinations Permutation – Order matters Math PRB #2 Combination – Order DOES NOT matter Math PRB #3

Other If in doubt quit out! (2nd MODE) Or reset your calculator: 2nd MEM (+ key), 7, 1, 2 ZOOM6 is standard 10 x 10 graph, ZOOMIN zooms in a lot, ZOOM4 zooms in a little—Use WINDOW key for specific settings