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:

...and your points
look like this:

...so 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:

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 = x^{2}
– 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

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

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".)