Solving Quadratic Inequalities

Example: Solve 3x2 + 3x - 6 < 0

Step 1: Go to and under Y1 enter
3x2 + 3x - 6.
Press .
You are graphing a quadratic function ,
so the graph should be a parabola .
Step 2: You want to determine where
the quadratic function is less than 0.
So you need to look at the graph and
determine
what part of the graph lies
below the x-axis or the line y = 0.
Step 3: The part of the graph that is
below the x-axis is the part that lies
between the x-intercepts.

To find these x- intercepts or zeroes ,
go to , the CALCULATE
menu, and select 2: zero .
Press .

To find the intercept on the left , use
the arrow keys to move the cursor to
the left of the point, press .
Then move the cursor to the right of
the point, press , and then
press
again.
The x-intercept is x= -2.

To find the intercept on the right, go
to , the CALCULATE
menu, and select 2: zero .
Press .

Then repeat the process used above.
The other intercept is x = 1.
Step 4: Remember - since you are
solving an inequality , the solution will
be an interval or the union of two
intervals.

The solution to this inequality is the
interval (-2, 1) or -2 < x < 1.
  Step 5: If you want to determine
where a quadratic is greater than 0,
you need to look at the graph and
determine what part of the graph lies
above the x-axis.
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