1. Completing the Square

2. Learning Targets  Learn how to complete the square  This allows us to go from Standard Form to Vertex Form  Solving for x in vertex form  Be able to freely change the form of any quadratic equation  Use knowledge of transformations to represent a function

3. How to Complete the Square

4. Most of the quadratics we work with are not perfect squares, so how do you find one?

5. How to Complete the Square Step 1: Subtract the “lonely” units Original Equation:

6. How to Complete the Square Step 2: Halve the remaining x’s Original Equation:

7. How to Complete the Square Step 3: Take those halves and rearrange them Original Equation: 1.5 x’s Notice how we have not lost any of our original equation

8. How to Complete the Square Step 4:Find out what new value was created and add it to both sides of the equation since we do not want to change anything Original Equation: Notice how we have still not lost any of our original equation

9. How to Complete the Square Step 5: Now figure out what base’s give us this new figure and write it as factored form Original Equation:

10. How to Complete the Square Step 6: Don’t forget about the “lonely” units!!! Original Equation:

11. How to Complete the Square Does this form look familiar?!?! We now have our original equation that was in Standard Form written in Vertex Form!!! But… We should check our work :)

12. Summary of Steps  Step 1: Subtract the “lonely” units  Step 2: Halve the remaining x’s  Step 3: Take those halves and rearrange them  Step 4:Find out what new value was created and add it to both sides of the equation, since we do not want to change anything  Step 5: Now figure out what base’s give us this new figure and write it as factored form  Step 6: Don’t forget about the “lonely” units!!!

13. Complete The Square Activity  In our table groups we will work on completing the square using algebra tiles  The goal is for you to see what this method does and why it works  Look for connections between the equation and the manipulative’s

14. Summary of Steps  Step 1: Subtract the “lonely” units  Step 2: Halve the remaining x’s  Step 3: Take those halves and rearrange them  Step 4:Find out what new value was created and add it to both sides of the equation, since we do not want to change anything  Step 5: Now figure out what base’s give us this new figure and write it as factored form  Step 6: Don’t forget about the “lonely” units!!!

15. Vertex Form -> Factored Form The last manipulation of forms is going from vertex form to factored form This requires us to solve for x once we are in vertex form

16. Example cont. Just like in our standard form we want to set the equation equal to zero in order to find our roots.

17. Example cont. Now we need to solve for x: Don’t forget to graph this and check your answers!

18. Quick Check

19. Overall Review

20. Homework  Worksheet #3