Graphing Overview: Absolute Values & Quadratics


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Graphing Overview (page 2 of 3)

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

Absolute values

This is where 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

...so you connect your dots like this:

WRONG!

You just sank yourself.

But if you remember to plot a negative x 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

...so you will connect your dots like this:

graph with correct line drawn

...which is the correct answer.

Quadratics

For quadratics, you need to plot more than just three points (try a minimum of five!), and you often need to plot negative x's, too. Three points just won't cut it anymore. For instance, suppose y = x² – 6x + 5. There are any number of things we can do to help us graph this. We can find the intercepts, which in this case are at (1, 0), (5, 0), and (0, 5), or the vertex, which in this case is at (3, –4). But we need to plot quite a few points, in order to get a good graph. Look at what often happens, if someone only uses three points: Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

T-chart	Incorrect graph

But this isn't right; parabolas look like smileys, not straight lines. (And these points don't even line up as a straight line!) Let's plot a few more points:

T-chart	Correct graph

Much better!

Note: A postive quadratic is a smiley, and a negative quadratic is a frowny. (Yeah, it's a dumb way of putting it, but you won't forget it now, will you?)

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Cite this article as:

Stapel, Elizabeth. "Graphing Overview." Purplemath. Available from
http://www.purplemath.com/modules/graphing2.htm. Accessed

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