Warm Up (5 Minutes) (-2,-2); Translated: Vertically 4, Horizontally -3 Graph the following points/lines… and their respective transformations: (-2,-2); Translated: Vertically 4, Horizontally -3 ( 1,3); Translated: Vertically -2, Horizontally 2 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 𝑓(𝑥)=𝑥2 to compare and contrast other quadratics 𝑓(𝑥)=𝑥2 is a standard quadratic with its vertex at the origin and commonly referred to as a parabola X F(x) -2 4 -1 1 2 Vertex: (0,0)

Parent Function: Quadratic How can we transform this function of: 𝑓(𝑥)=𝑥2 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:

Vertical Compress/Stretch: Horizontally… Transformation: Rule: Horizontal Shift: Vertical Shift: Reflect over x-axis: Vertical Compress/Stretch:

Horizontally… 𝑓 𝑥 =( 𝑥−2) 2

Horizontally… You tell me… 𝑓 𝑥 =( 𝑥+2) 2

Vertical Compress/Stretch: Vertically… Transformation: Rule: Horizontal Shift: Vertical Shift: Reflect over x-axis: Vertical Compress/Stretch:

Vertically… 𝑓 𝑥 = 𝑥 2 −2

Vertically… You tell me... 𝑓 𝑥 = 𝑥 2 +1.5

Reflect over the x-axis… Transformation: Rule: Horizontal Shift: Vertical Shift: Reflect over x-axis: Vertical Compress/Stretch:

Reflect over the x-axis…

Vertical Compress/Stretch… Transformation: Rule: Horizontal Shift: Vertical Shift: Reflect over x-axis: Vertical Compress/Stretch:

What does a Vertical Compress/Stretch look like?

Vertical Compress/Stretch A quadratic will have a normal shaped curve when 𝑎=1 (𝑥) 2 A quadratic will compress by a factor of 𝑎 when 𝑎>1 2 (𝑥) 2 A quadratic will stretch by a factor of 𝑎 when 0<𝑎<1 0.5 (𝑥) 2

Vertical Compress/Stretch: Final Table!!! Transformation: Rule: Horizontal Shift: Vertical Shift: Reflect over x-axis: Vertical Compress/Stretch:

Combining It All… 𝑓 𝑥 =𝑎 𝑥+ℎ 2 +𝑘 Vertical Shift Horizontal Shift 𝑓 𝑥 =𝑎 𝑥+ℎ 2 +𝑘 Vertical Shift Horizontal Shift (opposite value) Compress/Stretch Factor Compress if: 𝑎>1 Stretch if: 0<𝑎<1 (if 𝑎 is negative it will reflect over the x-axis)

This equation is known as the vertex form of a quadratic!!! 𝑓 𝑥 =𝑎 𝑥+ℎ 2 +𝑘 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 ℎ: x-axis location 𝑘: y-axis location

What is the function? ℎ=−2 𝑘=−1 𝑎=.25 𝑓 𝑥 =.25 𝑥−2 2 −1

What is the function? You tell me... ℎ=1 𝑘=−3 𝑎=2 𝑓 𝑥 =2 𝑥+1 2 −3

Going from equation to graph Graph these equations and label the vertex: 𝑓 𝑥 =− 𝑥−2.25 2 +3 𝑓 𝑥 =2 𝑥 2 −2.5

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