Thread: Finding the formula to a graph

1. Finding the formula to a graph

Please help me find the formula to these two graphs. Also show your steps and work to how you found the formulas. I already know how to find the amp and midline. What I am having problem is finding the "c" in the formula y = A sin (Bx + C) + h.

Thank you so much!

2. 1) It apears you MUST use the SINE functions. Great. What are the characteristics of the function y = sin(x)?

1a) Starts at zero: $0 = \sin(0)$
1b) It first goes in the positive direction.
1c) Period is $2\pi$
1d) Amplitude is 1

2) Now let's take a look at your graph.

2a) Starts at zero: $0 = \sin(0)$ - Good.
2b) It first goes in the positive direction. - Good.
2c) Period is $2\pi$ - Nope. We have $\frac{\pi}{14}$ I think. The drawing is not real clear.
2d) Amplitude is 1 - Nope. It appears to be 0.80

3) Okay, so how do we fix it?

3a) Starts at zero: $0 = \sin(0)$ -- y = sin(x)
3b) It first goes in the positive direction. -- y = sin(x)
3c) Period is $2\pi$ -- $\frac{2\pi}{\frac{\pi}{14}}\;=\;28.$ -- $y = \sin(28x)$
3d) Amplitude is 1 -- $y = 0.80\cdot \sin(28x)$

I think we're done.

3. Thank you so much for helping me with part 1, it was an excellent explanation . To be honest, I don't know where to start at for part 2. Is there such a formula for it? The lines does not seem to be heading up/down at a constant pace and makes steep slopes at the point above the midline. So can you confirm that this has no formula or is there a formula for it?

4. second graph looks like an attempt to sketch this ...