Lesson Overview:

 

• Completing Square to get the vertex form of Quadratic Functions

• Use Completing Square to find the standard form of Circle

• Writing equations of circle according to given information

• Solving nonlinear inequalities

 

Part A: Completing Square to get the vertex form of Quadratic Functions

Key Concepts: (x + b/2)^2 = x^2 + bx + (b/2)^2

https://www.youtube.com/watch?v=uF3YPpDSHBg&list=PL6S08t2cIqdL6GCO6SP6lLeHMRF93j-To&index=2&t=0s

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Example of SAT testing for converting to vertex form

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Real World Examples

This video shows a real-world example of converting quadratics to vertex using completing the square.

 

 

 

 

 

 

Conclusion:

After this lesson, students should be able to predict the shape of rational functions by using sign diagrams. After their predictions, they should be able to graph the functions on graph paper by following the basic rules learned. These skills can be used to predict the graph of rational functions when given the equation as shown in the example above.