Quadratics Unit Graphing Quadratics using Transformations (Vertex Form)

1. QUADRATIC
TRANSFORMATION
S
Unit 4

2. NOTES TO REVIEW
Please take out the following
worksheets/packets to review!
Absolute Value Activity
Function Transformation
Parent Function Transformation

3. DO NOW
𝑓 𝑥 = 𝑥 + 1 2 − 5
 Horizontal translation
 Vertical translation
𝑓 𝑥 = 2 𝑥 − 4 2
 Vertical dilation
 Horizontal translation
𝑓 𝑥 =
1
2
𝑥2 + 3
 Vertical dilation
 Vertical translation
𝑓 𝑥 = − 𝑥 − 5 2 + 2
 Reflection over x-axis
 Horizontal translation
 Vertical translation

4. TIPS FOR GRAPHING QUADRATICS
Use “squares” to graph
Remember that parabolas are
symmetric!
 Out 1, up 1
 Out 2, up 4
 Out 3, up ___
 Etc
Graphing with a Reflection
 Out 1, down 1
 Out 2, down 4
 Etc
Graphing with a Dilation
 Out 1, up 1∙a
 Out 2, up 4∙a
 Out 3, up 9∙a
 Etc
Example:
a=2 a= 1/2
 Out 1, up 2 Out 1, up 1/2
 Out 2, up, 8 Out 2, up 2

5. WHY DOES GRAPHING WITH
SQUARES WORK?
The h & k will move the parabola around the
graph.
The 𝑎𝑥2
term is what forms the shape parabola.
Therefore, you are technically just plugging in
x-values into 𝑎𝑥2
to form the parabola!

6. GRAPH QUADRATIC FUNCTIONS
𝑓 𝑥 = 𝑥 + 1 2
− 5
Vertex?
Domain?
Range?
X-Intercept?
Y-Intercept?

7. GRAPH QUADRATIC FUNCTIONS
𝑓 𝑥 = 2 𝑥 − 4 2
Vertex?
Domain?
Range?
X-Intercept?
Y-Intercept?

8. GRAPH QUADRATIC FUNCTIONS
𝑓 𝑥 =
1
2
𝑥2
+ 3
Vertex?
Domain?
Range?
X-Intercept?
Y-Intercept?

9. GRAPH QUADRATIC FUNCTIONS
𝑓 𝑥 = − 𝑥 − 5 2
+ 2
Vertex?
Domain?
Range?
X-Intercept?
Y-Intercept?

10. VERTEX
Finding the Vertex from the
Graph
•The highest or lowest point of
the parabola
•Very similar to finding the vertex
of an absolute value!
Finding the Vertex from the
Equation
•The x-coordinate is the
horizontal translation (h)
•The y-coordinate is the vertical
translation (k)
•The vertex is written at (h,k)

11. VERTEX FORM
𝑓 𝑥 = 𝑎 𝑥 − ℎ 2
+ 𝑘
“a” is the reflection/dilation
“h” is the horizontal translation
“k” is the vertical translation
The vertex is (h,k)
The graph open ______ if a>0 and opens ______ if a<0.up dow
n