+130 +130 +130 +130 +130 
+130 | y = 2 sin x + 3 | y = 2 cos x + 3 | |
| Wavelength | 2π | 2π |
| Midline | y = 3 | y = 3 |
| Amplitude | 2 | 2 |
| y-intercept | 3 | 5 |
First Graph: https://www.desmos.com/calculator/dloymhzsxx
Second Graph: https://www.desmos.com/calculator/komjqsqgfi
+130 ------------------------------------------------------------------------------------------------------------------
Question 1-
Desmos Graph: https://www.desmos.com/calculator/0ozgnesvrp (From checking afterward.)
a) Midline: y = -1
b) y-intercept: -1
c) Wavelength: π
d) Amplitude: 1
e) Does it start going up or down?: It begins moving upwards.
f) What is the equation?: y = 1 sin x -1
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Question 2-
Desmos Graph: https://www.desmos.com/calculator/ig7vrwjg8m (From checking afterward.)
a) Midline: y = 4
b) y-intercept: 4
c) Wavelength: π
d) Amplitude: 1
e) Does it start going up or down?: It begins moving downwards.
f) What is the equation?: y = -1 sin x + 4
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+130 Equation: y = 3 -4 sin x
1. "What is the least confusing way to write this?"
I'm not exactly sure what you mean by that, I apologize.
Are you asking about how can this equation can be rearranged? If so, I'm not entirely sure.
2. "What number does the minus sign belong to?"
The minus sign belongs to the four I presume.
3. "What will be the main features of this graph?"
Once again, not entirely sure what you mean here, I assume you mean the midline, y-intercept, etc?
a) Midline: y = 3
b) y-intercept: 3
c) Wavelength: 2π (From after checking the Desmos graph.)
d) Amplitude: 4
4. "What is the y-intercept?"
The y-intercept is 3.
5. "Is the y-intercept on the centerline?"
It seems to be. (From after checking the Desmos graph.)
6. "From the y-axis, will the graph start going up or down? How can you tell this from the equation?"
I assume it will begin downwards because of the -4 in the equation. Previously, the addition of the minus sign inflects the graph to move downwards initially instead of upwards into the positives. (Accurate after having checked the Desmos graph.)
After checking afterward, here is the graph. https://www.desmos.com/calculator/tmwabdozb0
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+130 Equation: y = sin x
https://www.desmos.com/calculator/sqqxxosznt
a) Midline: y = 0
b) y-intercept: 0
c) Wavelength: 2π
d) Amplitude: 1
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Equation: y = -sin x
https://www.desmos.com/calculator/pqi9uqbmyf
a) Midline: y = 0
b) y-intercept: 0
c) Wavelength: 2π
d) Amplitude: -1 (?) No, the amplitude is always positive. It stays +1
What I see from both of these graphs is they share similar properties almost entirely, except for the second graph being flipped. With that said, does that mean the amplitude will be considered -1? Or will it remain a positive always? Either way, they're incredibly similar graphs, but one appears to be flipped because of the negative.
EXCELLENT. If you times by minus -1 the graph flips over, (It reflects across the y axis)
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Equation: y = 3 sin x
https://www.desmos.com/calculator/uluaswag14
a) Midline: y = 0
b) y-intercept: 0
c) Wavelength: 2π
d) Amplitude: 3
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Equation: y = -3 sin x
https://www.desmos.com/calculator/qw3tpmqfhq
a) Midline: y = 0
b) y-intercept: 0
c) Wavelength: 2π
d) Amplitude: -3 (?) +3
Similarly, comparing these two graphs, the only noticeable difference is that the figure appears to be flipped because of the negative. Once again, I'm not sure if amplitude should ever be written in negatives, and if not, then the answer should be just the definite form of what is already written, I assume. I hope these are correct.
That is all great, you are learning really well.
+130 y= 4(sinx)-3 (I added the equation so it is with the answers - Melody)
a) Midline: y = -3
b) y-intercept: -3
c) Wavelength: 2π
d) Amplitude: 4?
This is the graph from afterward.
https://www.desmos.com/calculator/0znoabjdqu
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Melody:
I am here now so I willl add my response here.
Your answer is spot on.
You seem hesitant about amplitude:
Yes it is 4 and you can see that on the formula.
To get it from the graph find the highest y value and subtract the lowest y value and then halve it. (+1--7)/2 = 8/2 = 4
Or
get the highest y value and subtract the midline y value. In this case +1 - - 3 = 1+3=4
Make sure you underst this from the graph.
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New question: Get this one right and I will move onto a slightly new idea.
y=6+8sinx
what will be
a) midline
b) y intercept
c) wavelength
d) amplitude
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Peerless Cucumber: *Wave*
y=6+8sinx
a) Midline: y = 6
b) y-intercept: 6
c) Wavelength: 2π
d) Amplitude: 8
https://www.desmos.com/calculator/2miu9weqtv
Here is the graph!
+130 https://www.desmos.com/calculator/gg71ka6oqn
a) Midline: y = 5
b) y-intercept: 5
c) Wavelength: 2π
d) Amplitude: 1
These all are somewhat similar to y = sin x, however, when it becomes +5, it merely moves up 5 on the graph, and the logic seems consistent when replaced by a 2, 3, or any other number, for example. Whereas by changing the number it is multiplied by effects the amplitude?
