Solving Quadratic Inequalities
EXAMPLE: Solve 3x^2 + 3x – 6 > 0

Step 1: Press Y= Under Y_{1} 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 Y_{1} > 0, so let’s enter this under Y_{2} Place the cursor beside Y_{2}= Press the VARS key 

Step 3: Arrow over to YVARS We want to call up Y_{1} which is under 1:Function so press ENTER To select Y_{1} press ENTER again 

Step 4: To insert the inequality symbol , go to the TEST menu by pressing 2^{nd} 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 yvalues, which is what we are looking for since 3x^2 + 3x – 6 > 0 The x values are to the left and right of the xintercepts. 

Step 6: To find the xintercepts, 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 Now press ENTER one more time 

The xvalue 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 2^{nd} TRACE arrow down to 2: zero and press ENTER Use the arrow keys to
move the Then move the cursor to the right Now press ENTER one more time 

The xvalue for the intercept is 2 
So the solution for the inequality is
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