Question

I have a few questions about this equation>> y=3sin(6(x+2))+4
I know that the amplitude is 3
How would I find what the period is?
What is the horizontal shift? (left or right? and by how much?)
How would I find the midline?

Answer 1

@tkhunny I closed this on accident. I reopened it in the "Open Questions" section if you cannot reply on this one

Answer 2

Think on \(y = \sin(x)\)
Amplitude: 1
Period : \(2\pi\)
Midline: y = 0
Horizontal Shift; None

You recognized that \(y = 3\sin(x)\) results in an amplitude of 3.
Amplitude: 3
Period : \(2\pi\)
Midline: y = 0
Horizontal Shift; None

The midline shift is the only other easy part. That 4 is just kind of hanging out there. Once you see it, you are not likely to forget it. Thus \(y = 3\sin(x) + 4\) results in
Amplitude: 3
Period : \(2\pi\)
Midline: y = 4
Horizontal Shift; None

Are we making sense, so far?