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# Graphing a Quadratic Inequality - Concept

###### 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

inequality.

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.

Okay.

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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###### Carl Horowitz

B.S. in Mathematics University of Michigan

He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his step-by-step explanations are easy to follow.

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