Warm Up (5 Minutes)Graph the following points/lines…

and their respective transformations:

a) (-2,-2); Translated: Vertically 4, Horizontally -3

b) ( 1,3); Translated: Vertically -2, Horizontally 2

c) Transformed: Vertically -1, Horizontally 2, Increase slope by a factor of 1.5

4.1.2 How Can I Shift a Parabola

Learning targets for today: How can I shift a Parabola…

Vertically? Horizontally? Reflect over x-axis? Compress/Stretch the graph?

Vertex Form of a Quadratic

Parent Function: Quadratic

We are going to be using the following equation of to compare and contrast other quadratics

is a standard quadratic with its vertex at the origin and commonly referred to as a parabolaX F(x)

-2 4-1 10 01 12 4

Vertex: (0,0)

Parent Function: Quadratic

In our table groups we are going to fill out the rules for each

transformation…Transformation: Rule:Horizontal Shift:

Vertical Shift:Reflect over x-axis:

Vert. Compress/Stretch:

How can we transform this function of:

Horizontally…

Transformation: Rule:

Horizontal Shift:

Vertical Shift:

Reflect over x-axis:

Vertical Compress/Stretch

:

Horizontally…

𝑓 (𝑥 )=¿

Horizontally…

-4 -3 -2 -1 1 2 3 4

-4

-2

2

4

x

y

You tell me…

𝑓 (𝑥 )=¿

Vertically…

Transformation: Rule:

Horizontal Shift:

Vertical Shift:

Reflect over x-axis:

Vertical Compress/Stretch

:

2)()( hxxf

Vertically…

𝑓 (𝑥 )=𝑥2−2

Vertically…

-4 -3 -2 -1 1 2 3 4

-4

-3

-2

-1

1

2

3

4

x

y

You tell me...

𝑓 (𝑥 )=𝑥2+1.5

Reflect over the x-axis…

Transformation: Rule:

Horizontal Shift:

Vertical Shift:

Reflect over x-axis:

Vertical Compress/Stretch

:

2)()( hxxf

2)( xkxf

Reflect over the x-axis…

Vertical Compress/Stretch…

Transformation: Rule:

Horizontal Shift:

Vertical Shift:

Reflect over x-axis:

Vertical Compress/Stretch

:

2)()( hxxf

2)( xkxf

What does a Vertical Compress/Stretch look like?

Compress

Stretch

Vertical Compress/Stretch

A quadratic will have a normal shaped curve when

A quadratic will compress by a factor of when

A quadratic will stretch by a factor of when

Final Table!!!

Transformation: Rule:

Horizontal Shift:

Vertical Shift:

Reflect over x-axis:

Vertical Compress/Stretch

:

2)()( hxxf

2)( xkxf

Combining It All…

Compress/Stretch Factor

Stretch if: (if is negative it will reflect over the x-axis)

Horizontal Shift(opposite value)

Vertical Shift

𝑓 (𝑥 )=𝑎 (𝑥+h )2+𝑘

Vertex Form

This equation is known as the vertex form of a quadratic!!!

We call it this because it clearly gives us the vertex of its parabola

: x-axis location: y-axis location

𝑓 (𝑥 )=𝑎 (𝑥+h )2+𝑘

What is the function?

-4 -3 -2 -1 1 2 3 4

-4

-3

-2

-1

1

2

3

4

x

y

h=−2

𝑓 (𝑥 )=.25 (𝑥−2 )2−1

𝑎=.25𝑘=−1

What is the function?

-4 -3 -2 -1 1 2 3 4

-4

-3

-2

-1

1

2

3

4

x

y

h=1

𝑓 (𝑥 )=2 (𝑥+1 )2−3

You tell me...𝑘=−3𝑎=2

Going from equation to graph

𝑓 (𝑥 )=− (𝑥−2.25 )2+3

Graph these equations and label the vertex:

𝑓 (𝑥 )=2 (𝑥 )2−2.5

Homework

I will make a worksheet that relates to the lesson terminology and processes.