Completing the Square

Algebra IIProfessor Martin

Lecture 6.19

LECTURE 6.19 – PART I

When will I see this in calculus?

Perfect Square Trinomial

x

x ax

ax

𝒙𝟐

Example #1: Convert the function into vertex form.

Step 1:

Step 2:

Step 3:

Step 4:

Vertex form

Step 5:If we want to solve…

What is the key idea?

=

x

x ax

ax

𝒙𝟐

Completing the square write a quadratic function as a perfect square trinomial to solve or write in vertex form

INTERMISSION

Check for Understanding

• Annotate your notes – record key take-aways and questions

• Turn-and-talk: clarify misunderstandings

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

LECTURE 6.19 – PART II

How is completing the square useful for any quadratic equation?

, where a, b, and c are real numbers and

END OF LECTURE 6.19

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)….”

Check for Understanding

• Solve classwork problems with your partner• Ask your partner if they can answer your non-

HOT questions• Record HOT questions