Naming Polynomials

There are many different polynomials. They each have different names oddly enough.
 What follows is a list of the different types.
Degree                                                                  Terms
0 (constant)                                                           monomial
1 (linear)                                                                binomial
2 (quadratic)                                                          trinomial
3 (cubic)                                                                quadrinomial
4 (quartic)                                                              polynomial
5 (quintic)
6 (nth)

Graphing y=a|x-h|+k

y=a|x-h|+k is the equation for absolute value.
The vertex for your graph is (H,K)

The A determines whether your graph will open up or down. If your A is negative it will open down. If your A is positive it will open up. The A will also determine the slope. If A is say, -3, then the graph would have a slope of -3/1 and would open downward.

The H determines the horizontal location of the vertex and the K determines the vertical location. However it is opposite of what would be expected with the horizontal variable in the fact that if H is negative then it moves to the right and if it's positive then it moves to the left.

The green graph is the graph of the new function. It is a translation of the blue graph moved one unit down and 2 units left.

Types of Systems

 When graphing, there are many different equations. First off is the most well known, linear. The equation of a linear line is y=x. This is a consistent/ independent. This equation generally looks like this when graphed:

There are others such as the parent equation y=x^2. When graphed this will form a parabola, a u-shaped line.It is a consistent/ independent graph. Then similar to that is the Absolute Value equation or y=|x|. This ends up as v-shaped line. It is a consistent/ independent graph.

The last three are Square Root equation, Exponential equation, and Rational equation. Square Root is y=rx.  This is a consistent/ independent. It's graph looks like this:

 'r' stands for radical and the symbol looks like this:

Exponential has the equation of y=2^x. This a consistent/ independent line. It looks like this:

Finally rational has an equation of y=1/x. This is an inconsistent graph. It looks like this: