Transformations of Basic Graphs

NOTICE: MINUS 3 moves the graph to the RIGHT 3...

also, MINUS 3 happens INSIDE the main part of the equation...

in this case... INSIDE the parentheses being SQUARED.

HOW TO

shift a graph horizontally

(side to side,

left or right...)

RIGHT:

NOTICE: PLUS 3 moves the graph to the LEFT 3...

also, PLUS 3 happens INSIDE the main part of the equation...

in this case... INSIDE the parentheses being SQUARED.

HOW TO

shift a graph horizontally

(side to side,

left or right...)

LEFT:

Multiple Choice

What is the equation of the BLUE graph?

• y = (x+2)²

• y = (x-2)²

• y = (x+4)²

• y = (x-4)²

Multiple Choice

What is the equation of the RED graph?

• y = (x+2)²

• y = (x-2)²

• y = (x+4)²

• y = (x-4)²

NOTICE: PLUS 3 moves the graph UP 3...

also, PLUS 3 happens AFTER the main part of the equation...

in this case... AFTER the part where x is being SQUARED.

HOW TO

shift a graph vertically

(up or down...)

UP:

NOTICE: MINUS 3 moves the graph DOWN 3...

also, MINUS 3 happens AFTER the main part of the equation...

in this case... AFTER the part where x is being SQUARED.

HOW TO

shift a graph vertically

(up or down...)

DOWN:

Multiple Choice

What is the equation of the BLUE graph?

• y = (x+4)²

• y = (x-4)²

• y = x² + 4

• y = x² - 4

Multiple Choice

What is the equation of the RED graph?

• y = (x+4)²

• y = (x-4)²

• y = x² + 4

• y = x² - 4

investigate the example provided carefully -- you will be asked to do one on your own next...

HOW TO

shift a graph horizontal

AND vertically!

Multiple Choice

What is the equation of the RED graph?

• y = (x+3)² + 2

• y = (x-3)² + 2

• y = (x+3)² - 2

• y = (x-2)² + 3

• y = (x+2)² + 3