Well then, all you need to know is this:
(x+y)^2 = (x+y) (x+y) = x^2 + xy + yx + y^2 = x^2 + 2xy + y^2
Whenever you have crap in parenthesis squared, you need to multiply each term to each of term, you can't just square each and leave it at that. So basically, you multiply the first and the first together, then the first and the second together, then the second and first together, and then the second and the second, and then simplify.
To do the inverse of this operation (this is called factoring), you find two numbers that multiply to give the number on the far right (if put in order of powers from greatest to least, as shown), that also add up to become the number in the middle term, as shown below.
x^2 + 10x + 16 = (x+?) (x+?) = (x+8) (x+2)
Oh, and the graph of y = x^2 is called a parabola. By default, the vertex is at (0,0), and both sides go up in a curve. modifying this equation, by doing things such as y = -x^2 + 4, change the graph. In this case, the vertex would be at (0,4) and would have arrows going downward. On the topic of graphs, another important concept you need to know is that if an equation has a fraction, whatever is on the bottom cannot equal zero. So, in the instance of y = (x+4) / (x-2), x cannot equal positive two, as that would make the denominator zero. On the graph, at the line x = 2, there would be what's called an asymptote (or vertical asymptote), meaning that, well, I don't know how to explain it in words. Just graph the function and you'll see what it does. You'll know what I'm talking about. It's basically the whole concept of infinity, both positive and negative infinity, at infinitesimally close points to that line in the X direction. I'm sorry if I'm confusing you with this, just disregard that last sentence if you don't understand, because that's actually going into one of the basic concepts of calculus, which is not going to be on the SAT.
And then there's the imaginary number, i. Basically, i is the square root of -1. It doesn't really exist, but it kinda does. If you have i^2, then you really have -1. i^3 is -i, and i^4 is positive 1. Since anything times 1 is itself, the cycle repeats itself past i^4. If you run into questions with i in them, either skip over it, or see if you can manipulate i to get rid of it. If it's too intimidating, just treat it just as you would with any variable, such as x.
Lastly, there's logarithms. Just use your calculator for that. But, for an explanation as to what a logarithm is, it's really just a fancy way of rewriting exponents. If log(x) = y, then 10^y = x. In the same way, ln and e are opposites of each other, and cancel each other out. If ln(x) = y, then e^y = x.
There's also matrices, but I hate those. There's a bunch of rules for them that you have to remember, and I don't remember them. Even with that being said, I still made a 97% on my final exam for that class. They're not that important.
That's algebra 2 in a nutshell. I don't know why they draw it out for a whole year, it really isn't necessary. There's only a few new concepts, the rest is just remembering crap from algebra 1.
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