Completing the Square

1. Completing the Square Algebra II Professor Martin Lecture 6.19

2. Lecture 6.19 – Part I

3. When will I see this in calculus?

4. Perfect Square Trinomial x ax ax x

6. Example #1: Convert the function into vertex form. Step 1: Step 2: 

7. Step 3: Step 4: Vertex form

8. Step 5: If we want to solve…

9. What is the key idea? x = ax ax x Completing the square  write a quadratic function as a perfect square trinomial to solve or write in vertex form

10. Intermission

11. Check for Understanding • Annotate your notes – record key take-aways and questions • Turn-and-talk: clarify misunderstandings

12. In your notes, add the following questions in the cue column, next to where you have written the answer in the notes section: • What is a perfect square trinomial? • What is completing the square and why do you use it? • In the cue column next to each step, describe what is being done in each step of completing the square

13. Lecture 6.19 – Part II

14. How is completing the square useful for any quadratic equation? , where a, b, and c are real numbers and

15. 

18. End of lecture 6.19

19. Check for Understanding Write a one-sentence summary describing the derivation of the quadratic formula. Start with “The quadratic formula is derived from (comes from)….”

20. Check for Understanding • Solve classwork problems with your partner • Ask your partner if they can answer your non-HOT questions • Record HOT questions