1-11 Completing the Square

1-11 Completing the Square

Completing the Square to Rename Quadratics

Warm Up

A basketball is dropped from the roof of a building.

On the next slide, you will select each true statement about this graph

Multiple Select

Select ALL statements that are true

• When time=0, height=0 ft

• The basketball falls at a constant rate

• This is a quadratic function

• This is a linear function

• When time=0, the ball is 50 ft off the ground

Notebook: Learning & Habit Objectives

Learning: I will complete the square to rename quadratics

Habit: I will work each step neatly line-by-line

Success Criteria

• I can identify perfect square trinomials

• I can transform any quadratic into perfect square factored form

Notebook: Perfect Square Trinomials

A perfect square trinomial is represented by a perfect square in factored form.

For example, x²+6x+9 = (x+3)²

Notebook: Make a Perfect Square (will do in class)

Add C such that you have a perfect square trinomial:

Example x²+14x+ ___

Example x²-8x+ ___

Example x²+10x+___

What pattern do you notice?

Notebook: Steps for Completing the Square

• For trinomials that are not perfect squares, we can transform them into perfect squares using this procedure:

• 1) Keep A and B on the same side and move C over the =

• 2) Take half of B and square it. Add this number to both sides

• 3) Now the A and B side is a perfect square, so factor it

• 4) Move the c term back over the = to join your perfect square

Notebook: Example

• 1) Move C: x²-14x = -40

• 2) B/2 squared = 49

• 3) Add 49 to both sides x²-14x+49= 9

• 4) Factor: (x-7)² = 9

• 5) Bring back c: (x-7)² - 9

Multiple Select

Exit Ticket A: Select ALL that are perfect squares

• (x+5)(5+x)

• (x+5)(x-5)

• (x-3)²

• x²+8x+16

• x-3²

Multiple Choice

Exit Ticket C: Complete the Square

$$x^2+10x=-13$$  

• $$\left(x+100\right)^2-83$$  

• $$\left(x+10\right)^2+3$$  

• $$\left(x-5\right)^2+8$$  

• $$\left(x+5\right)^2-12$$