1. Graph
1.1. end behavior
1.1.1. a > 0
1.1.1.1. n=even #
1.1.1.1.1. x -> - ∞ y -> ∞
1.1.1.1.2. x ->∞ y->∞
1.1.1.2. n= odd #
1.1.1.2.1. x -> -∞ y -> -∞
1.1.1.2.2. x -> ∞ y->∞
1.1.2. a < 0
1.1.2.1. n= even #
1.1.2.1.1. x -> -∞ y -> -∞
1.1.2.1.2. x -> ∞ y-> -∞
1.1.2.2. n = odd #
1.1.2.2.1. x -> -∞ y-> ∞
1.1.2.2.2. x-> ∞ y->-∞
1.2. mutiplicity
1.2.1. 1
1.2.1.1. crossing
1.2.2. 2
1.2.2.1. touching
1.2.3. 3
1.2.3.1. crossing & flexing
2. Solving
2.1. Linear function
2.1.1. graphing
2.1.2. linear system
2.1.2.1. graphing
2.1.2.1.1. the intersecting part
2.1.2.2. elimination
2.1.2.3. substitution
2.2. Quadratic function
2.2.1. magic cross
2.2.2. quadratic formula
2.2.3. complete the square
2.2.3.1. x^2+bx+(b/2)^2
2.2.4. graph
2.3. Factor
2.3.1. GCF
2.3.1.1. Example
2.3.1.1.1. 2x^2+12x = 2x (x+6)
2.3.2. Factor common binomial
2.3.2.1. Example
2.3.2.1.1. x (x+1)+2(x+1) = (x+1)(x+20
2.3.3. Factor the products
2.3.3.1. Example
2.3.3.1.1. 12x^2 = (4x)(3x)
2.3.4. P/Q method
2.3.4.1. remainder theorem
2.3.4.1.1. f(x) = (x-a)q(x)+r(x)
2.3.4.2. factor theorem
2.4. Division
2.4.1. long division
2.4.2. synthetic division
2.4.2.1. synthetic substitution
2.4.2.1.1. x-c
2.4.3. P/Q method
2.5. Multiplication
2.5.1. distributive property
2.6. Addition
2.6.1. combining like terms
2.7. Subtraction
2.7.1. combing like terms
3. Definition
3.1. Types
3.1.1. Constant
3.1.1.1. no roots
3.1.1.1.1. unless y=0
3.1.1.2. degree 0
3.1.1.3. slope = 0
3.1.1.4. form: y=x
3.1.2. Linear
3.1.2.1. degree 3
3.1.2.1.1. 0 / 1 / 2 roots
3.1.2.2. one real root
3.1.2.3. degree 1
3.1.2.4. slope = constant
3.1.2.4.1. slope = rise / run
3.1.2.5. form
3.1.2.5.1. slope-intercept form
3.1.2.5.2. point-slope form
3.1.2.5.3. standard form
3.1.3. Quadratic
3.1.3.1. degree 2
3.1.3.2. form
3.1.3.2.1. vertex form
3.1.3.2.2. point-slope form
3.1.3.2.3. intercept form
3.1.3.3. axis of symmetry
3.1.3.3.1. x=-b / 2a
3.1.4. Cubic
3.1.4.1. 1~3 roots
3.1.4.2. y=ax^3+bx^2+cx+d
3.2. function
3.2.1. y=anx^n+an-1x^n-1+......+a0
3.2.1.1. a = real #
3.2.1.1.1. coefficient
3.2.1.2. a0 = y-intercept
3.3. an expression consisting of variables and coefficients
4. Order of Operation
4.1. brackets
4.1.1. parenthesis
4.1.1.1. exponents
4.1.1.1.1. multiplication / division