Lesson Overview:

 

• Use Sign Diagram to solve polynomial inequalities  

 

Part A: Using Sign Diagrams to solve polynomial inequalities

These videos teach how to graph Piecewise and Step Functions:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Now that we know the most important rule to keep in mind when using the sign diagram, let's do an example. First, we need to find the zeros of the inequality as seen in part A. of this example.

 

 

 

 

 

 

 

 

 

 

 

 

 

In part, B. draw the Sign Diagram and make the zeros points on the line. To start predicting the graph, we have to a plug in a value, that is not a point on the graph, into the inequality; in this example, the value we use is 1. After finding the sign of that value, we then find the signs of the intervals by using the rule above. 7 and 0 have an odd power, so their signs are opposite of the sign next to them, making them both positive. The last sign stays the same as the sing next to it because the factor it came from had an even power of 2.

 

 

 

 

 

 

 

 

 

 

 

 

In part C., because the sign of our inequality is greater or less than zero, the shaded intervals above are our answer, and the zeros may also be answers to the inequality so they are shaded in as well with brackets around them. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Inequalities in Test Questions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Real World Connection 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Conclusion:

In conclusion, you can use Cosine Law to solve for triangles when you are lacking one side or one angle. Make sure you label your triangle appropriately and to remember that your calculator is your best friend. You can use Sine Law to solve for triangles by knowing two sides and one angle or two angles and one side. Simply plug in the appropriate numbers into the formula and solve. It is important to keep in mind that sometimes it may be necessary to use Sine Law along with Cosine Law to solve for a triangle.