Can you help with my math homework?

Question

How can you predict what a graph will look like given an equation. (linear graphs, parabolas, and other kinds of functions) How do the different forms an equation can be written in tell you different information about what the graph will look like?

Answer 1

You can easily tell what a function's graph will look like by determining the degree of the function.  The degree of a function is the power of the term with the highest power.  If there is a ^3 somewhere in the function, then it is a 3rd degree function, ^2, a second degree, and so on.  Any first degree function will be linear, any second degree function will be parabolic, and any 3rd degree function will be squiggly, for lack of a better word.  Second, the sign of the term with the highest degree can tell you if the function approaches positive or negative infinity as x approaches infinity.  Finally, for second degree and higher functions, there is the intercept form, which is the fully factored form of the function; it tells you exactly where the function crosses the x-axis.