PLEASE, Study the Rules & do the Examples first, then do ...
Transcript of PLEASE, Study the Rules & do the Examples first, then do ...
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 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