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Solving Quadratic Inequalities

EXAMPLE: Solve 3x^2 + 3x – 6 > 0

Step 1: Press Y=
Under Y1 enter the polynomial
3x^2 + 3x – 6
Then press GRAPH
We want to find where the
polynomial is greater than 0.
Step 2: Go back to Y=
We want to know where Y1 > 0,
so let’s enter this under Y2
Place the cursor beside Y2=
Press the VARS key
Step 3: Arrow over to Y-VARS
We want to call up Y1 which is
under 1:Function so press ENTER
To select Y1 press ENTER again
Step 4: To insert the inequality
symbol , go to the TEST menu by
pressing 2nd MATH
Arrow down to 3:> and press
ENTER
Step 5: Now enter 0 and press
GRAPH
The horizontal lines show which
x- values have positive y-values,
which is what we are looking for
since 3x^2 + 3x – 6 > 0
The x- values are to the left and
right of the x-intercepts.
Step 6: To find the x-intercepts,
go to the CALCULATE menu by
pressing 2nd TRACE
Arrow down to 2: zero and press
ENTER
Step 7: To find the intercept on
the right
, use the arrow keys to
move the cursor to the left of the
intercept (left bound) and press
ENTER

Then move the cursor to the right
of the intercept (right bound) and
press ENTER

Now press ENTER one more time
(for guess)

The x-value for the intercept is 1
Step 8: To find the intercept on
the left, we repeat the process.
Go to the CALCULATE menu by
pressing 2nd TRACE arrow down to
2: zero and press ENTER

Use the arrow keys to move the
cursor to the left of the intercept
(left bound) and press ENTER

Then move the cursor to the right
of the intercept (right bound) and
press ENTER

Now press ENTER one more time
(for guess)

The x-value for the intercept is -2

So the solution for the inequality is

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