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Math Analysis First Chapter (Chapter 1 (1.1-1.4 (Forms of a linear…

- - - - Standard/General Form: ax+by=c
        
        a, b, and c are integers
        
        a > 0
      - Slope-intercept Form
        
        y = mx + b
      - Point-slope Form
        
        y - y1 = m( x-x1 )
      - Intercept Form: x/a + y/b = 1
        
        a = x intercept
        
        b = y intercept
    - - Parallel: slopes are equal
      - Perpendicular: slopes are opposite reciprocals
    - - Distance Formula: [ ( x2 - x1)^2 + (y2 - y1)^2]^1/2
      - Midpoint Formula: [ ( x1+ x2)/2 , (y1 + y2)/2 ]
    - - Substitution
      - Elimination
      - Graphing
      - Matrices
    - - One Solution: Obtain exactly one value for each variable (one intersection)
      - No Solutions: Obtain an equation that is never true (0 = 5) (parallel lines)
      - Infinitely many equations: Obtain an equation that is always true (0 = 0) (same line)
  - - - a is a real #
      - a and b are real numbers
      - Rule: ai + bi = ( a + b )i
      - Rule: If a > 0, then √-a = i√a
      - Rule: a + bi and c + di are only equal if a=c and b=d
      - a + bi and a - bi are complex conjugates (simplify rational expressions)
  - - - Standard: y = ax^2 + bx + c
      - Vertex: y = a( x - h )^2 + k
    - - Factoring
        
        Set equation equal to 0 --> 2. Factor --> 3. Set each factor equal to 0 --> 4. Solve the equation
      - Quadratic Formula
        
        Set equation equal to 0 --> 2. Use the quadratic formula -->
        
        Simplify to solve for x
      - Completing the Square
        
        Divide both sides by coefficient of x --> 2. Subtract constant term from both terms --> 3. Add square of 1/2 of coefficient of x to both sides --> 4. Factor and solve