The general technique for
graphing quadratics is the same as for graphing
linear equations.
However, since quadratics graph as curvy lines (called "parabolas"),
rather than the straight lines generated by linear equations, there are
some additional considerations.

The most basic quadratic
is y = x^{2}.
When you graphed straight lines, you only needed two points to graph your
line, though you generally plotted three or more points just to be on
the safe side. However, three points will almost certainly not be enough points for graphing a quadratic, at least not until you are very experienced. For example, suppose a student computes these three points:

Then, based only
on his experience with linear graphs, he tries to put a straight
line through the points.

incorrect
graph

He got the graph wrong.
You, on the other hand, are more careful.

You find many points:

That last point has a rather
large y-value,
so you decide that you won't bother drawing your graph large enough to
plot it.

But you plot all
the other points:

Even if you'd forgotten
that quadratics graph as curvy parabolas, these points will remind you
of this fact.

You draw a nicely
smooth curving line passing neatly through the plotted points:

Unlike the careless student,
you just got the graph right.

Some students will
plot the points correctly, but will then connect the points with
straight line segments, like this:

incorrect
"segment" graph

This is not correct. You
do still need a ruler for doing your graphing, but only for drawing the
axes, not for drawing the parabolas. Parabolas graph as smoothly curved
lines, not as jointed segments.