Among other things, typically you will look for:* Maxima and minima.
* Inflection points (also found with calculus).
* Regions where the graph goes upwards, and regions where it goes downwards.
All of these can be found using calculus.
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If the two at the end of these are exponents, like x^2, then these graphs would be reflections across the x-axis. Their graphs would be two parabolas. f(x) pointing up, and g(x) pointing down.
The way you can use graphs of polynomial functions to show trends in data is by comparing results between different functions. The alternation between the data will show the trends. Time can also be used to show the amount of variation.
There are a couple of graphs you could use. A pie graph or a bar graph.
Functions (lines, parabolas, etc.) whose graphs never intersect each other.
Bar graphs and line graphs do not. Straight line, parabolic, and hyperbolic graphs are graphs of an equation.