MATHGOTSERVED 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. 2. 3. 2-4 COMPLEX NUMBERS OPERATIONS
2-5 COMPLEX NUMBERS OPERATIONS
2-5 COMPLEX NUMBERS OPERATIONS