DODDS 1

Properties of Exponents & Radicals

PLEASE, Study the Rules & do the Examples first, then do the Assignments. The goal is Not to just get the assignments done, but for you to thoroughly Master the Required Skills or Re-Learn the Skills you Struggle with.

DODDS 2

Rationalizing Radicals.

DODDS 3

DODDS 4

Absolute Value Equations.

**Solve **Solve

Solve

DODDS 5

Multiplying polynomials using Three Different Methods

DODDS 6

Graphing a Piecewise Function

Quadratic Function (Polynomial of degree 2) Shape of the graph of a quadratic function is a Parabola. Three parabolas are shown below with important points labeld.

The graph of a quadratic funciton: - can open either upward or downward

- always has a vertex which is either the maximum or minimum

- always has exactly one y-intercept

- can have 0, 1, 2 x-intercepts

* A parabola is symmetric about a line through the vertex called the axis of symmetry.

* A quadratic function can be written in Transformation Form which is 2

f x y a bx h k

* In Transformation Form, the vertex is ,h

kb

and line of symmetry is h

xb

.

* A quadratic function can be written in Polynomial Form which is 2 f x y ax bx c

* In Polynomial Form, the vertex is , 2 2

b bf

a a

and line of symmetry is

2

bx

a

.

Solution graph

DODDS 7

Complex Numbers: The complex number system contains a number, denoted 1i , such that 2 1i .

Every complex number can be written in standard form a bi .

DODDS 8

Factoring Polynomials Using Real Numbers.

**Always, First Factor out any Greatest Common Factor (GCF) existing in All the Terms of polynomial.

Note, some polynomials may NOT have a GCF.

Binomial (2-Terms) Trinomial (3-Terms) Quadrinomial (4-Terms)

1. Difference of Two Squares Factor by Grouping

Ex: 3 22 5 10x x x 2 2 a b a b a b

2 2 5 2x x x

22 5x x

Ex: 4 3 22 14 2 14x x x x

3 22 7 7x x x x

22 7 1 7x x x x

22 7 1x x x

2 7 1 1x x x x

Factor 22 22a ab b a b

22 22a ab b a b

Ex: 22 12 36 6x x x

Ex: 224 20 25 2 5x x x

When you have 2ax bx c

If 1a

Ex: 2 3 18x x 6 3x x

If 1a

Ex: 22 5 12x x 2 3 4x x

Ex: 249 25 7 5 7 5x x x

GCF

group

DODDS 9

Use Completing the Squre

to Change from Polynomial Form to Transformation (Vertex) Form.

Solve a Quadratic Equation by Completing the Squre.