# QUADRATICS

### By: Indroop Bassi

## Table of Contents

**Introduction:**

- Parabolas

- Second Differences

- Transformations

**Types of Equations:**

- Vertex Form

- Factored Form

- Standard Form

**Vertex Form**

- Equation In Vertex Form

- Mapping Notation

- Determine the Equation From a Graph

**Factored Form**

- Multiplying Binomials

- Special Products (binomials)

- GCF and Factor by Grouping

- Simple Factoring

- Factoring Quadratic Expression/Special Cases

- Solve by Factoring

- Graphing Factored Form

**Standard Form**

- Quadratic Formula

- Discriminant

- Completing the square

- Graphing from standard form

**Word Problems:**

- Height

- Profit

- Geometry

- Number Problems

- Economic

## Introduction

## Second Differences

## Parabolas

Axis of Symmetry: line that splits the parabola in half (x value)

Optimal Value: y value, can be a MAXIMUM or MINIMUM value

x intercepts: the zeroes

y intercepts: graph crosses y axis

## Transformations

The (-h) is the horizontal translation. It moves the parabola either to the LEFT or RIGHT. (when it's positive, moves to left. When it's negative, moves to right)

The (k) is the vertical translation. It moves the parabola UP or DOWN. When k is negative, it moves down. When k is positive, it moves up.

The (a) is the vertical stretch and is reflected in the x-axis if there is a negative sign. It also stretches the parabola.

Vertex (h,k)

Once you know the vertex, you can use the step pattern to find the rest of the points to complete the graph.

## Types of Equations

**1. Vertex Form:**y=a(x-h)² +k

**2. Standard Form:** y= ax²+bx+c

**3. Factored Form:** y= a(x-r)(x-s)

## Vertex Form

## Solving Given Vertex Form

## Isolating for x

1. Transfer -50 to the other side of the equal sign. Moving it over changes it to +50

2. Divide both sides by 2

3. Square root both sides of the equation to get rid of ²

4. Transfer -5 to the other side of the equal sign to have x by itself. (Make sure -5 changes to +5 after moving it to the other side)

5. Solve

## Graphing Vertex Form

## Factored Form

## Expanding (Factored to Standard)

F = First Term

O = Outside Term

I = Inside Term

L = Last Term

## Simple Trinomials

## Complex Trinomials

## Common Factoring

## Specials Cases (Perfect Square & Difference of Squares)

## Factoring by Grouping

## Graphing Factored Form

## Standard Form

## Solving Using Quadratic Equation

1. Find the value of a,b & c with the equation provided

2. Use the quadratic formula to sub in the values

3. Solve to find x intercepts

## Discriminant

## Completing the Square

## Graphing Standard Form

## Word Problems

## Height

## Profit

## Area

## Number Problem

## Economic

2. Use revenue formula

3. Write the equation

4. Solve