# Quadratics

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## Quadratics

__Quadratics Part 1__

1) Intro to Quadratics

2) Different parts of a Parabola

- Axis of Symmetry
- (x)Optimal Value (y)
- Zeros
- Vertex
- y-intercept

3)Vertex Form.

Graphing Vertex Form

4) Finding the Equation and Analyzing

Vertex Form

5) Factored Form → y= a(x-r)(x-s).

__Quadratics Part 2__

1) Factoring Complex Trinomials

2) Factoring Simple Trinomials

3) Factoring Perfect of Squares

4) Factoring Difference of Squares

5) Factoring common factors

6) Expand and simplify .

7)Graphing Quadratics using x-intercept.

__Quadratics Part 3__

1) Completing the Square.

2) Quadratic Formula

3) Discriminant Formula

## 1) Intro to Quadratics.

## Different parts of a Parabola

Like

1) vertex -that is the point of the parabola at its maximum (max) or minimum (min) value

2)Axis of symmetry- it divides the parabola into 2 equal half's

3)Optimal Value- the the y co-ordinate of the vertex

4) Zero- it can be called a (zero/x-intercepts/roots) is when the graph goes though the x axis

5)y-intercept is a parabola is where the graph crosses the y-axis

## Graphing Vertex Form

This is a vertex with a positive equation

-Vertical transformation is a (something #) of a unit that opens up or down

-Horizontal transformation is a (something #) of a unit that moves left or right

-a number that is factored by a vertical or compressed

## Finding the Equation and Analyzing Vertex Form.

y=a(x-h)^2+k

The 2 beside the the power of 2 for example The vertex of a Parabola is (-2,2) and the x-intercept is (2,4). What is the equation of the of the parabola.

1) Write the equation down y=a(x-h)^2+k

2) Fill n the valuable in the equation 4=a(2+2)^2+23)

3) than you would have to do the brackets 4=a(2+2)^2+24)

4)than you would have to do the power of 2 4=a(4)^2+25)

5) than do take away the 2 and do it to the other side too 4=a(16)+26)

6)than divide the the 2 side by 2 2=16a =7)2/2=16/28) a=8

Therefor the equation will be y=8(x+2)^2=2

## Factored Form

## Quadratics Part 2

## Factoring Complex Trinomials

## Factoring Simple Trinomials

## Factoring Perfect of Squares

## Factoring Difference of Squares

## Factoring common factors

## Expand and simplify

## Graphing Quadratics using x-intercept

## Quadratics Part 3

## Completing the Square

1) First you have to take the # on the right side out y=(x^2-10)+20

2) Now you want to see the middle # that is 10, you have to divide the by 2 and the square root it to 2. 10/2= 5 52=25

3) Now you would add the 25 in and subtract 20 too. y=(x^2-10+25-25)+20

4)After you have to take out the -25 in the brackets and put beside the 20. y=(x^2-10+)+20-25

5)Now you have to subtract the 20-25 so that would be -5.(x^2-10+)-5

6)Lastly. you would have to see want you can divide with 1x. it will be 1 and 1. Also you would have to find a # that will add to the middle number and that will multiply to the last number. (x+5)^2-5

## Quadratic Formula + standard Formula

## Discriminant Formula

y=ax2+bx+c

y=x^2+6x+5

a=1

b=6

c=5

1) 6^2-4(1)(6)

2) 36- 24

3) =12