# Quadratic Relationships

### By: Harman Virk

## LEARNING GOALS

## First/Second Differences

## LinearIf the first differences are the same (in this case all the differences are 6) it means that it's linear. | ## QuadraticAll of the second differences are the same and this is an example of quadratics. | ## NeitherThis is neither linear or quadratic. |

## Transformations

## Determining an equation using 2 points

Learning Goal 3

## SUMMARY OF THE UNIT

## The Step Pattern

## How the step pattern works

The odd numbers (1,3,5) are multiplied by the "a" value. In the first example the numbers are multiplied by 1, in the second example the numbers are multiplied by 2 because that is the value of "a".

## GRAPH

## WORD PROBLEM USING VERTEX FORM

**The flight path of a firework is ****modeled**** by the relation h=-5(t-5)****2****+127 where h is the height, in metres, of the firework above the ground and t is the time, in seconds, since the firework was fired.**

**a) What is the maximum height reached by the firework?**

The maximum height is 127 m.

** **

**b) How many seconds after it was fired does the firework reach this height?**

The firework reaches 127 m after 5 seconds.

## VIDEO

Video Using Transformations