# Quadratics Relationships

### By : Anmol Saggu

## What is Quadratics

## Where are Parabola used in daily life

## Table of Contents

1 __Introduction__

- Analyzing quadratics (second differences)

- Introduction to parabolas

-Transformation

2 __Types of equations__

- Vertex form

- Factored form

- Standard form

3 __Factored form__

- Common factoring

- Factoring simple trinomials

- Factoring complex trinomials

- Special cases

- Difference of squares
- Perfect square

- Factoring by grouping

- Graphing factored form

4__ Vertex form__

- To find an equation when only given the vertex

- Isolating for x

- Graphing vertex form

5 __Standard form__

- Completing the square (standard to vertex)

- Graphing from standard form

- Solving using quadratic equation

- Discriminant

## Analyzing quadratics (second differences)

If none of them are same then it's neither

## Introduction to Parabolas

**Curve.**Which in Math is called a

__Parabola__.

A Parabola can either open upwards or downwards depending on the A value. If the A value is a **positive number** then the parabola will open **upwards **and if the A value is a **negative number** then the parabola will open **downwards**.** **

__Main components of a parabola__

Vertex - where the axis of symmetry and parabola meet

The axis of symmetry - divides the parabola into two equal halves

Optimal value - the y co-ordinate of the vertex/ highest or lowest point

X- intercepts - the zeroes

Y- intercept - when the graph crosses the y-axis/ y ≤ optimal value or y ≥ optimal value

## vertex

## X- intercepts/Zeros

**factored form.**

## optimal value

## Axis of Symmetry

Formula of AOS : A+B/2

## step pattern

## Desmos!! It's a great app to check your parabola answers on your electronic device

## quadratic Transformations

**Horizontal Translation - It is a type of translation in which the parabola can be moved up or down depending on the value of "K"**

**Vertical Translation**: It is a type of translation in which the parabola can be moves right or left depending on the value of "H"

**Vertical Stretch/Compression**: vertical stretch is when the parabola stretches or expands. it is only possible if the "A" value is bigger than 1. Vertical compression is when the parabola gets thin and small. That happens when the "A" value is less than 1.

**Vertical Reflection**: A vertical reflection is when the parabola flips or reflects vertically

## 3 Different Types of Quadratic Forms

**1.Vertex Form - **y= a(x-h)^2+k

**2.Standard Form** **-** y=a(x-r) (x-s)

**3.Factored Form** **- **ax^2+bx+c