1. T5.1d To Graph Vertical Translation
T5.1d To Graph Vertical Translation

2. As a group, find the equation of this graph
As a group, find the equation of this graph. I will call on someone, please make sure you have it:
y = 4
sin (x) 2

3. Active Learning Assignment?
Amplitude……….._______
Vertical Translation_______
Period Frequency…_______
Period Length……._______
Phase shift……….._______

4. * * LESSON: Standard form for Sine Function: y = a*sin b * (x – h) + k
Standard form for Cosine Function: y = a*cos b * (x – h) + k
Today we will be looking at how “k” affects the sin and cos curves. Let’s look at Desmos. * *
y = a*sin b * (x – h) + k REALLY comes from:
y – k = a*sin b * (x – h)

5. Graph y = 2 sin (x) + 3 OR could be: y = 3 + 2 sin (x) NOT 5! 2 y =3 1
Amplitude……….._______
Vertical Translation_______
Period Frequency…_______
Period Length……._______
Phase shift……….._______ 2 5
y =3 3 1 1
Beginning ¼ ½ ¾ End 2π
1 Period π
“0”
Max
“0”
Min
“0”

6. This is the y axis: → (x = 0)
Graph y = 2 sin (x) + 3
Please pay attention: 5
This is the x axis:
(y = 0) → 3 1
This is the y axis: → (x = 0)
Do not “highjack” the coordinate axes and put your labels on them!!! For example, in this problem, DO NOT CHANGE THE X AXIS TO “3”. You must show your own translation or shift!!!

7. Graph y = – 2 + 5 cos (x) OR could be: y = 5 cos (x) – 2 NOT 3! 5
Amplitude……….._______
Vertical Translation_______
Period Frequency…_______
Period Length……._______
Phase shift……….._______ 5
y = -2 3 1 -2 -7
Beginning ¼ ½ ¾ End 2π
1 Period π
Max
“0”
Min
“0”
Max

8. As a group, find the equation of this graph
As a group, find the equation of this graph. I will call on someone, please make sure you have it: 6
y = 2
cos (x) 4
+ 3 4

9. Graph y = ½ sin ¼ (x) + 3 ½ y = 3 ¼ 1 Period “0” Max “0” Min “0” 3
Amplitude……….._______
Vertical Translation_______
Period Frequency…_______
Period Length……._______
Phase shift……….._______ 3
y = 3
Beginning ¼ ½ ¾ End
1 Period
“0”
Max
“0”
Min
“0”

10. Active Learning Assignment:
Graph I Handout: odds