# 07 Transformations Investigation Activity 1

- Author:
- Jason Lee

## Instructions

Move the sliders for a and b in the applet and answer the following questions based on your observations.

## y = x² vs y = (x - a)² + b

## Question 6.1

Shift the slider value for a from a = 0 to a = 4. Describe the resultant transformation of y = x² to y = (x - 4)².

## Question 6.2

With the slider value of a kept at 4, shift the slider value for b from b = 0 to b = -6. Describe the resultant transformation of y = (x - 4)² to y = (x - 4)² - 6.

## Question 6.3

What are the coordinates of the turning point of the curve with equation y = (x - a)² + b?

## Question 6.4

Describe a two-step transformation from y = x² to y = x² - 8x + 8. Show your working clearly.

## Question 6.5

What is the technique you have used in Question 6.4 to work out the two-step transformation?

## Question 6.6

Describe the replacement of variable in each step of your two-step transformation in Question 6.4.