Transforming the Eight Parent Graphs

Vertical Compression

Vertical Dilations

Vertical Stretch

Transform!

(Click Me)

The Parameters for Graphing Form

( h, k ): The Key Point

The value of aPositive: Same Orientation If it Increases: Vertical Stretch

Negative: Flipped If it Decreases: Vertical Compression

Parent Graph: When a=1, h=0, and k=0

They do the same thing for every function!

Graphing Form for the First 5 Parent Graphs

( h, k ): The Key Point

The value of aPositive: Same Orientation If it Increases: Vertical Stretch

Negative: Flipped If it Decreases: Vertical Compression

Parent Graph: When a=1, h=0, and k=0

Quadratic Cubic

Hyperbola Square Root

Exponential

3y a x h k

1x hy a k y a x h k

x hy ab k

2y a x h k

Quadratic Function

2y xParent Equation

Graphing Form

2y a x h k

Example: Quadratic

New Equation:

23 4y x

y = 4

x = 3

Transformation: Shift the parent graph three units to the right and four units up.

(3,4)

Cubic Function

3y xParent Equation

Graphing Form

3y a x h k

Example: Cubic

3 5y x

y = 5

x = 0

Transformation: Flip the parent graph and shift it five units up.

New Equation:

Transformation:

(0,5)

Hyperbolic Function

1xy

Parent Equation

Graphing Form

1x hy a k

Example: Hyperbola

14 3xy y = -3

x = -4

Transformation: Shift the parent graph four units to the left and three units down.

New Equation:

Transformation:

(-4,-3)

Square Root Function

y xParent Equation

Graphing Form

y a x h k

Example: Square Root

6y x y = 0

x = -6

Transformation: Shift the parent graph six units to the left.

New Equation:

Transformation:

(-6,0)

Exponential Function

2xy Example of a Parent Equation

Graphing Form x hy ab k

Example: Exponential

53 2 2

xy

y = 2

x = 5

a = 3

Transformation: Shift the parent graph five units to the right and two units up. Then stretch the

graph by a factor of 3.

New Equation:

Transformation:

(5,2)

Linear Function

y xParent Equation

Graphing Form

y a x h k

Unless specified, you do not need to have the answer in y=mx+b form!

Point: Slope:(h,k) a

Example: Linear

y a x h k

y = 4

x = -6

Slope = ½

Transformation: A line with slope ½ that passes through the point (-6,4).

12 6 4y x New Equation:

Slope Point

(-6,4)

Absolute Value Function

y xParent Equation

Graphing Form

y a x h k

Absolute value can be found

in the calculator:

a) MATH

b) Right to NUM

c) 1. abs(

Example: Absolute Value

y = 4

x = -3

Transformation: Flip the parent graph and shift it three units to the left and four units up.

Transformation:

3 4y x New Equation:(-3,4)

Equation for a Circle

2 2 25x y Example

Graphing Form

2 2 2x h y k r

Center: Radius:(0,0)

Center: Radius:(h,k)

25 5

2r r

Example: Circle

y = -1

x = 4

Transformation: A circle centered at (4,-1) whose radius is 4.

Transformation:

2 24 1 16x y

New Equation:

Center:

Radius:

(4,-1)

16 4NO!Is a circle a function?

(4,-1)