Post on 15-Feb-2016
description
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.