Transcript How do we solve quadratic inequalities?

How do we solve quadratic
inequalities?
Do Now: What is the difference
between an equation and an
inequality?
What are we trying to find
when we solve inequalities?
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We are trying to find the values of x that
make the inequality true.
If we are trying to solve the inequality
x2-x-6<0, then we want the values of x
that would make y negative in the
equation y=x2-x-6
We can look at the graph and see that
this is true when -2<x<3
But how can we solve it
algebraically?
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First we want to
factor.
(x-3)(x+2)<0
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Next we solve for
values of x that
make the
expression equal
zero
x=3, x=-2
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Now we put this on
a number line
2
x -x-6<0
-2
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Since the inequality is simply less than zero,
then we use an open circle to mark the
points.
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3
Note: If the inequality was less than or equal to
zero, the the circle would be solid
Now, we pick a value in each section; x<-2, 2<x<3, 3<x and plug it into the inequality.
2
x -x-6<0
-2
+
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3
-
+
(-3-3)(-3+2)=(-6)(-1)=6
(0-3)(0+2)=(-3)(2)=-6
(4-3)(4+2)=(1)(6)=6
Finally, we express our answer in one of two
ways:
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Symbolically: -2<x<3
Graphically: Shade in the correct part of the
number line
Example
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Given: x2-2x-20>4
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Find the solution set.
Graph the solution set on a number line.
Summary/HW
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If the problem is a quadratic, is there
always a set pattern of positives and
negatives?
HW pg 101, 1-16 even