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Solving Quadratic Inequalities
Example: Solve 3x^{2} + 3x  6 < 0
Step 1: Go to and under Y1 enter 3x^{2} + 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 xaxis or the line y = 0. 

Step 3: The part of the graph that is below the xaxis is the part that lies between the xintercepts. 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 xintercept 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 xaxis. 
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