4th Blog...

I'm pretty much lost on what material is in what section right now but I know how to find an equation from a graph, shifts and everything. I've even got a picture as an example.


I apologize for the picture quality but its good enough.

The process of finding an equation from a graph is basically the same as having to sketch a draft from an equation.

Everything you need to sketch a graph can be found inside of the graph. You need an A and a B and need to know whether it is positive or negative or sine or cosine, and whether or not it shifts. Everyone of these things can be deduced just from looking at the picture.

First you check to see if its a sine or cosine function and if its positive or negative. In this case, it looks like it would be cosine but its really a positive sine function with a vertical shift.

Its positive because the graph opens upward after passing the y axis and its sine because it doesn't cross the axis at its amplitude.

That leads us to the next step which is finding the Amplitude and Period of the graph.

To find the Amplitude just count how many points are from the point that crosses the y axis and the highest point on the graph, here its 2, not 3.

Now the Period is a little tricky. You need to count to the fifth point on the graph and multiply that point by 2pi.

Its kind of hard to explain how to count the points without physically showing it but I'll try. You start with the point that crosses the y axis, that's your first point, next you count the point that is highest on the graph, the next is going to be parallel to the first and then you count the lowest point on the graph, and so on and so forth until you have a total of five points.

Here its going to be 4.

Then you just multiply 4 x 2pi and that will give you B. Which comes out to be 1/2 pi or pi/2 they are the same thing.

Alright so far we have found that: our graph is a positive sine function with a vertical shift
our Amplitude is 2
and our B is pi/2

NOW WE CAN WRITE OUR EQUATION!! :O

Okay so we have everything we need, so lets get started.

We know its positive and its sine so we can start with: y = sin

Our Amplitude is 2 sooooo it then becomes: y = 2 sin

Next our B is pi/2: y = 2 sin pi/2x

Now we have to represent the vertical shift. It shifts up by one point so it will be represented by a - 1 in the equation. You always put the opposite sign of the way it shifts.

When your done its going to look a little like this: y = 2 sin (pi/2x - 1)

Hope it helped.

My apologies if it didn't...