Functions, Quadratics, and Binomials all tied into one

        A function is when a single variable, called the dependent variable, for instance Y, is in terms of atleast one other variable, called the independent variable, and for each X-value there can only be one Y value. Y=X² is considered a function because Y is put in terms of X. "X + Y = 3" is considered a function because you could move either the X or Y to the other side and have one variable in terms of another, such as Y=3-X. Functions are written usually as f(X)=, or as Y=, such as f(X)=7X+3, or Y=7X+3.

Tip: A simple way to graphically test if it is a function is to use the vertical line test. If you can put a vertical line anywhere on the graph and it does not intersect the graph more than once, it is a function.

        Graphing where the function is not of the first power can be complicated because you could have X2 and also have X to the first power in it as well. Example: Y=2X2+8X+8. When its highest power is 2, then the function is known as a Quadratic. In functions where the highest power of X was 1 you could find out what the Y intercept is by putting it in the form of Y=mX+b, it is possible, but only sometimes, to find the zeroes* of the function.

* Zeroes are where the function crosses the x-axis, where Y=0

        Finding the zeroes of Quadratics is where binomials will come into play. To get a quick refresher on binomoials then go here. If you were to multiply one binomial by another binomial you would end up with an X raised to the second power, which would then classify it as a Quadratic. Only some quadratics are actually the product of 2 simple binomials. Generally speaking, while learning Algebra and going over factoring and quadratics, most likely the quadratics will be the product of two binomials. The process of figuring out what two binomials were multiplied to get the quadratic is called factoring . Factors are the two binomials you get after factoring a quadratic. You can factor functions that are bigger (raised to higher powers) than quadratics, and you would still end up with factors, maybe not two though.

        When you are trying to find the zeroes of a quadratic and it does not look like it factors nicely into two binomials, there is an alternative. You could use something called the Quadratic Formula.

For a quadratic equation in the form aX²+bX+c=0, then to find its zeroes you would use the Quadratic Formula.