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Graphing a Quadratic Inequality - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Solving a quadratic inequality by graphing is not difficult if you remember the basics of graphing a quadratic equation. When graphing quadratic inequalities, first graph the quadratic equation then pick a point that is not on the parabola itself and plug it into the original inequality. If the statement is true, shade in the area where that point lies. If the statement is false, shade in the other area.

Solving a quadratic inequality graphically.

What we do with a quadratic inequality is very
similar to what we do with a linear

Basically what we want to do is sketch
the curve and then choose a test point
to see which side we're
going to shade.
We'll do a very simple
example behind me.

What I have is Y is less than X squared.
Basically what we want to do is view
this as an equality, and then sketch
the graph.

So we know that Y equals X squared is just
a parabola, vertex at the origin.
Just like with linears, this
one is strictly less than.
That tells us we have a data line because
things on this line aren't going
to satisfy this inequality.
So we basically sketch our parabola with
a dotted line, and then choose a test point.

Your point can be anything you want.
Just make sure it is not on the parabola.
So choose something safe.
We'll look at the point, say, 0, 1 and
all we have to do is plug that in and
see if we get a true or false statement.

We plug in 0, 1, what we end up with
is 0 is greater than 1. That's a
false statement.
So that tells me that this point inside doesn't
actually satisfy this inequality.
So I shade the other portion.

If I got a true statement I would shade
that side, false statement shade the other.
So what we end up with is everything
outside of this parabola.

Now solving a quadratic inequality, just
plot your graph, choose your test point
and shade the appropriate region.

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