## Introduction

Graphing a quadratic equation by plotting many points on the line. All quadratic equations have an axis of mirror symmetry and a minimum or maximum point.

We discuss the transformations, vertical shift, reflection, and stretch.

## The form y=ax²+c

The solutions, axis of symmetry, and vertex of a quadratic equation where b=0.

## The y=ax²+bx

The solutions can be found by first factorising the equation.

## Factorisation

Factorising a quadratic equation explained geometrically.

## Graphing y=(x+n)(x+m)

Finding the solutions, axis of symmetry, and vertex of a factorisable quadratic equation.

We discuss how to design a quadratic equation by placing the solutions and vertex.

## A Perfect Square

Perfect quadratic squares have equals solutions and the curve touches the x-axis

## Transformations II

Transformation of a quadratic equation such as stretch, reflection, vertical and horizontal displacment are explored.

## Completing the Square

We discuss completing the square for quadratic equations to find the solutions.

## Completing the Square and Transformation

Completing the square shows that all quadratic curves can be formed by applying transformation to the simplest quadratic curve y=x²