# Quadratics Unit

### By: Hashim Mohamed

## Table of Contents

__Introduction__

Intro to Parabolas

First and Second Differences

__Equation Forms__

Factored Form

Standard Form

Vertex Form

__Vertex Form:__ y=a(x-h)^2 +k

-Axis of Symmetry

-Optimal Value

-Transformations

-Step Pattern

-X-int or zeroes

-Finding an equation for a parabola

__Factored Form:__ y=a(x-r) (x-s)

- X-int or zeroes

- Axis of symmetry

- Optimal value

__Standard Form:__ y=ax^2+bx+c

-Quadratic Formula

-axis of symmetry

-Optimal value

- Using completing the sq to turn into vertex

-Factoring

-Common

-Simple

-Complex

-Perfect Squares

- Difference of squares

## PARABOLAS

Here are some important terms to remember, this is what makes up a parabola.

**Axis of Symmetry: **It's in the middle of your parabola. It helps to find your vertex.

**Vertex Point: **This is the curve of the parabola. It's the direction of where it faces.

**Optimal Value: **This is the value of your vertex.

## FIRST AND SECOND DIFFERENCES

Below is a chart of an example of the first and second differences.

## EQUATION FORMS

Vertex form: h= a(x-h)2 +k

Factored form: a(x-r) (x-s)

Standard form: ax2+bx+c=0

## VERTEX FORM

Ex. y= -2(x-2)^2 +3

**Vertical Reflection: **If it's a - the parabola will open downwards. If it's positive it will open upwards.

**Vertical Stretch: **This effects the step pattern instead of doing the basic step pattern routine it will double instead look below.

**Horizontal Translation: **This moves the parabola left or right. It's also the part of the vertex.

**Vertical Translation: **This moves the parabola up or down. It's also a part of the vertex.

## GRAPHING VERTEX FORM

## FINDING AN EQUATION FOR A PARABOLA

## FACTORED FORM

## STANDARD FORM

## COMMON FACTORING AND EXPANDING/SIMPLIFYING

## SIMPLE TRINOMIAL FACTORING

You can use trial and error which is a method known for finding the terms by taking a guess and seeing if its correct. We'll use that in complex factoring as well.

## COMPLEX TRINOMIAL FACTORING

## PERFECT OF SQUARES & DIFFERENCE OF SQUARES

Perfect Squares must follow the formula of (a+b) (a+b).

To see if its a difference of squares you must check for:

1. If the term is a square

2. If there is a - in between the two numbers.

## COMPLETING THE SQUARE AND TURNING IT INTO VERTEX FORM

## QUADRATIC FORMULA

The formula is below with an example.