Quadratics
Quadratic Relations
Quadratic Expressions
Quadratic Equations
- Common Factoring
1.Expanding Polynomials
- Factoring Complex Quadratic expressions
- Transformation of Quadratics
- Transformations of a Quadratic Relation
1.Linear vs Quadratic Equations
- Factored form of a Quadratic Relation
- Solving for Quadratic Equations
- Standard to Vertex Form
- Graphing using X-intercepts
- Quadratic Formula
The Quadratic Relation:
- Vertex: The maximum or minimum of the Parabola
- Axis of Symmetry: Vertical line that divides the parabola into 2.
- Parabola: The shape of the quadratic expression.
Quadratic Relation:
Vertex Form:
Steps into graphing an quadratic relation:
Step 1: Find the transformations.
Step 2: Find the new vertex
Step 3: Create a new set of values for the vertex
Step 4:Graph
- or - = Vertical Reflection
a= vertical stretch or compression
h= Horizontal translation
k= Vertical translation
If it is a negative, it is a vertical reflection (upside down)
a > 1 = vertical stretch
0<a<1= vertical compression
h makes the graph move left or right
- means it goes left and - makes it go right
k makes the graph go up or down
-means it goes down and + makes it go up
Solve:
Standard Form
Factored Form
Expanding Polynomials means to multiply factored form to get it into standard form.
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expanding (multplying)
Factoring Polynomials means to divide standard form to get to factored form
Factored Form
Standard Form
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expanding(multiplying)
Factoring( dividing)
We would use FOIL to multiply the polynomials
FOIL means First, Outer, Inner, Last, meaning the first numbers get multiplied, the outer numbers get multiplied, the inner numbers get multiplied, and the last numbers get multiplied.
The Outer numbers are the first and last numbers, and the inner numbers are the second and third numbers.
3.Factoring Quadratic Expressions
Standard Form
Factored Form
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Factoring and simplifying
Multiplying
Factoring equations involve finding a multiple of a and c multiplied that adds to b
Standard to vertex form involves finishing the square,
Finishing the square involves this forumla:
Finishing the square requires the x to be 0, so divide x by whatever the number is.
use the formula to find a number that will be positive and negative.
Move the negative to the outside. Multiply by the number infront if there is one.
Solve, but your answer should look like this:
y=(x-h)^2 +k
Solving for quadratic equations includes making sure the LS=RS
Graphing using X-Intercepts means using factored form to find the vertex by find the AOS.
AOS means area of symmetry, otherwise, the middle. The equation would look like this to find it:
The quadratic formula should be used when an equation cannot be factored.
It looks like this:
Factoring this equation involves breaking the B term into 2 parts and then to factor by grouping.
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Step 1: Find the new transformations
Vertical Stretch: 4
Vertical Translation: 4 up
Horizontal Translation: 8 units right
Step 2: Find the new vertex
(8,4) This is the vertex because the vertical translation plus the horizontal translation will give you the vertex.
Step 3: Create a new set of values for the vertex
x=1
x=2
Step 4: Graph
Solve: 
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First, multiply 6x and x.
6 time x= 6x^2
Then, Multiply 6 and 9
6 times 9= 54
After, do -5 times x
-5 times x= -5x
Lastly, do -5 times 9
-5 times 9=-45
Your terms should look like this:
6x^2+54-5x-45
Add all common terms and it should end like this:
6x^2 -5x +11
Solve: 
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First, move all the numbers beyond the = to the other side:
Second, multiply 12 by 4 and find out what multiples into that and adds into your b value.
12x4= 48
8x6=48
8+6=14
Thirdly, simplify it. 
GCF for the 1st bracket:4m
GCF for the 2nd bracket: 4
