PRECALCULUS  
UNIT 2: POLYNOMIAL FUNCTIONS AND RATIONALS
Overview of Polynomials
  Polynomials:
Definition(meaning what is?): A polynomial function is a function that can be written in the form  f(x)=anxn+an-1xn-1+…a1x+a0
where n is a positive integer and an to a. are real numbers with an not being equal to zero.

Degree of a Polynomial
Definition( meaning of what is) The degree of a polynomial is the highest exponent of all the terms.

Naming Polynomials by Degree
Degree 1 (Linear Function ): A polynomial of degree 1 is known as a linear function. It can be written in the form y=mx+b
Degree 2 (Quadratic Function): A polynomial of degree 2 is  known as a quadratic function. The quadratic function can be written in different forms. Below are the forms of a quadratic function
Standard form y=ax^2+bx+c  (Best form for finding the y-intercept=c)
Vertex form y=a[b(x-h)]^2+k  (Best form for finding the vertex and consequently the shifts.
Degree 3(Cubic Functions) A polynomial of degree 3 is know as a cubic function
  
2-1 Quadratic Functions
Definition  (Meaning) of a Function:
A Quadratic function is a polynomial of degree 2. 
 Given a quadratic function with vertex form y=a[b(x-h)]+k, and standard form y=ax2+bx+c
The properties are as follows
Vertex (h,k)
Opening: Opens up if a>0, and opens down if a
Extrema: Maximum if a>0, minimum if a<0. Extrema at h=-b/2a, and value at k = f(-b/2a)
Shift: h units left for f(x +h) and h units right for f(x-h), k units up for f(x)+k, and k units for f(x)-k
Axis of symmetry: x=h or x=-b/2a
y-intercept: value of c or find f(0)
x-intercept: find x for f(x)=0
Domain: (- ꚙ,ꚙ)
Range: Opens up [h, ꚙ) Opens down (-ꚙ,h]
 
VIDEO TUTORIAL: QUADRATIC FUNCTIONS
VIDEO TUTORIAL: QUADRATIC FUNCTIONS
2-2 POLYNOMIAL FUNCTIONS OF HIGHER DEGREES

Polynomials of higher degrees can be generated when you are provided with sufficient information concerning the zeros. 
  
VIDEO TUTORIAL ON WRITING POLYNOMIALS WITH GIVEN ROOTS
2-3 RATIONAL ROOTS LONG &SYNTHETIC  DIVISION REMAINDER THEOREM
VIDEO TUTORIAL ON OPERATION ON FUNCTIONS
GALLERY OF SOLVED PROBLEMS
  1. how to write find polynomial least degree functions with integer coefficients  with given roots
  2. how to write polynomials integer coefficients given roots least degree integer
  3. End behavior leading coefficient test kuta polynomials how to rise fall left right
2-4 COMPLEX NUMBERS OPERATIONS
2-5 COMPLEX NUMBERS OPERATIONS
2-5 COMPLEX NUMBERS OPERATIONS