1. 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

2. 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

3. 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)

4. 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:

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

6. Horizontally…
𝑓 𝑥 =( 𝑥−2) 2

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

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

9. Vertically…
𝑓 𝑥 = 𝑥 2 −2

10. Vertically…
You tell me...
𝑓 𝑥 = 𝑥

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

12. Reflect over the x-axis…

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

14. What does a Vertical Compress/Stretch look like?

15. 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

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

17. 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)

18. 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

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

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

21. Going from equation to graph
Graph these equations and label the vertex:
𝑓 𝑥 =− 𝑥−
𝑓 𝑥 =2 𝑥 2 −2.5

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