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Graphing Overview (page 2 of 3)

Sections: Straight lines, Absolute values & quadratics, Polynomials, radicals, rationals, & piecewise

Absolute values

This graph is a good example of a context in which you really need to remember to pick negative x's for your T-chart. Otherwise, it is very easy to forget that an absolute value graph is not going to be just a straight line.

For instance, suppose y = | x |. And suppose you only chose positive x-values, so your T-chart looks like this:


T-chart with values listed



...and your points look like this:


graph with three points plotted you connect your dots like this:




You just sank yourself.

But if you remember to plot a negative x-value or two, your T-chart will look like this:


T-chart with more values



...and your points will look like this:


graph with five points plotted you will connect your dots like this:


graph with correct line drawn

...which is the correct answer. (For further information, study the lesson on "Graphing Absolute-Value Functions".)   Copyright Elizabeth Stapel 1999-2011 All Rights Reserved


For quadratic functions, you need to plot more than just three points (more like a minimum of at least five points), and you often need to plot negative x's, too. Three points just won't cut it anymore. For instance, suppose they give you y = x2 6x + 5. There are any number of things you can do to help yourself graph this. You can find the intercepts, which in this case are at (1, 0), (5, 0), and (0, 5); or you can find the vertex, which in this case is at (3, 4). But mostly you need to plot quite a few points. Look at what often happens, if someone only uses three points:

T-chart Incorrect graph
T-chart with values WRONG!

But that graph above isn't right; parabolas look like "smilies", not like straight lines. (And, if you look closely, the plotted points don't actually even line up as a straight line!) So you'll want to plot a few more points:

T-chart Correct graph
T-chart with more values graph with correct line drawn

Much better!

Note: A postive quadratic is a "smilie", and a negative quadratic is a "frownie". (Yeah, it's a dumb way of putting it, but you won't forget it now, will you?) (For further information, please study the lesson on "Graphing Quadratic Functions".)

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Cite this article as:

Stapel, Elizabeth. "Graphing Overview." Purplemath. Available from Accessed


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