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A standard form is the common acceptable way of presenting a mathematical equation.

Equations with one degree of freedom are linear equations.
Equations with more than one degree of freedom are called polynomial equations.
These equations are considered non-linear.
Both linear and polynomial equations have different characteristics.
LINEAR EQUATIONS: STANDARD FORM
Components of a standard form equation with one degree of freedom
Ax   +  B   =  0
variable
constant
     Ax +  B  = 0
integer
integer
Standard Form
Explanation and example of solving equations with one-variable.

Rule: 

  • A & B are all real numbers
  • X is unknown value
  • A cannot be zero

Rule: 

  • Integer A, cannot be neg.
  • A effects the variable x
  • It has one solution
Converting standard form (one -variable)
Ax   +  B   =  0

Equation to Standard Form

5x - 8 = x - 9

                        5x - 8 = x - 9      
                 5x - 8 + 9 = x - 9 + 9  --add 9 to both sides   
                          5x + 1 = x + 0  --subtraction rule
                         5x + 1  = x          
                   5x - x + 1 = x - x  --subtract x from both sides                     5x - x + 1 = 0               
                          4x + 1 = 0  --updated to standard form
m
(x   -     )
 
x

1

TWO-VARIABLE  EQUATIONS: STANDARD FORM
Components of a standard form equation with two-variables
Ax  +  By =  C
variables
Ax  -  By  =  C
constant
integers
Standard Form
Explanation and example of converting two-variables into standard form

Rule: 

  • A & B are all real numbers
  • C is a constant
  • A effect x  &  B effects y

Rule: 

  • Integer A, cannot be neg.
  • A cannot be zero
  • B cannot be a fraction
Converting standard form (two-variable)
Ax  +  By =  C

Equation to Two-Varible Standard Form

2y = -3x + 6

            2y = -3x + 6
 3x + 2y  = -3x + 3x + 6  --add 3x to both sides
 3x + 2y  = 0 + 6
3x + 2y = 6  --updated standard form
QUADRATIC FORM: STANDARD FORM
Components of the standard form with two degrees of freedom
2
Ax   +  Bx  +  C  =  0
variables
constant
Ax   -  Bx  +  C  =  0
2
Coefficient of x
Coefficient of x
2
Standard Quadratic Form
Explanation and example of converting equations to standard quadratic form.

Rule: 

  • A is the coefficient of x
  • Varibles must be on one side
  • One side must be zero (0)

2

Rule: 

  • B can be non-zero or zero
  • C is a constant value
  • C can be a non-zero or zero
Convert equation into standard form (quadratic form)
Ax    +   Bx  +  C  =  0
2

Equation to  Standard Quadratic Form

2

-x   - 3x - 6 = 5x - 8

 -x   - 3x - 5x - 6 = 5x -5x -8  --subtract 5x from both sides
   -x   - 3x - 5x -6 =  0 -8  --combine like-terms
            -x    - 8x - 6 =  -8  --addition rule
     -x    - 8x -6 + 6 = -8 + 6  --add 6 from both sides   
             -x   - 8x + 0 = -2 
                     -x   -8x = -2
             -x   - 8x + 2 = -2 + 2
             -x   - 8x + 2 = 0  --updated equation                   
2
2
2
2
2
2
2
2
CUBED FORM
Components of a standard form equation with three degrees of freedom

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