+

Completing the Square

+Practice factoring the following using the algebra tiles above:

x2 + 5x + 6

x2 + 4x + 4

x2 + 6x + 9

x2 + 8x + 16

click on to check your work…

+#1) x2 + 5x + 6

+#1) x2 + 5x + 6

+#1) x2 + 5x + 6

(x + 3) (x + 2)

+x2 + 4x + 4

+#2) x2 + 4x + 4

+#2) x2 + 4x + 4

(x + 2)(x + 2) = (x + 2)2

+#3) x2 + 6x + 9

+#3) x2 + 6x + 9

+#3) x2 + 6x + 9

(x + 3)(x + 3) = (x + 3)2

+#4) x2 + 8x + 16

+#4) x2 + 8x + 16

+#4) x2 + 8x + 16

(x + 4)(x + 4) = (x + 4)2

+What do #2, 3 & 4 have in common when you built them?  

+What do #2, 3 & 4 have in common when you built them?  They all made squares!!!

+Try factoring 4x2 + 8x + 4.  

What do you notice?

+Try factoring 4x2 + 8x + 4.  

What do you notice?

+Try factoring 4x2 + 8x + 4.  

What do you notice?

It’s still a square!!

(2x + 2)2

+All of the above examples are

considered perfect square trinomials.  Being able to

rewrite a trinomial in "perfect square" form allows you to solve for it using the square root method instead of the

quadratic formula.  

+Solve each of the following equations:A.  x2 + 4x + 1 = 0 B.  (x + 2)2 = 3

+Solve each of the following equations:A.  x2 + 4x + 1 = 0 B.  (x + 2)2 = 3

+Solve each of the following equations:A.  x2 + 4x + 1 = 0 B.  (x + 2)2 = 3

You ended up getting the same answer!

+Which method do you think was more straight forward? A or B?

+Build a square (the best you can) to factor x2 + 4x + 1

+Build a square (the best you can) to factor x2 + 4x + 1

+What do you need to “add” to

complete your square?

+You needed to borrow 3 tiles…

+How will you write this

algebraically?

+x2 + 4x + 1 + 3 – 3

x2 + 4x + 4 – 3

+How will you now write this in

“factored” form?

x2 + 4x + 4 – 3

+How will you now write this in

“factored” form?

x2 + 4x + 4 – 3 =

(x +2)2 - 3

+Practice completing the square on the following expressions:

x2 + 6x + 5

x2 + 8x + 5

4x2 + 8x + 1

+Practice completing the square on the following expressions:

x2 + 6x + 5 = x2 + 6x + 5 + 4 - 4

x2 + 8x + 5

4x2 + 8x + 1

+Practice completing the square on the following expressions:

x2 + 6x + 5 = x2 + 6x + 5 + 4 – 4

= (x + 3)2 - 4

x2 + 8x + 5

4x2 + 8x + 1

+Practice completing the square on the following expressions:

x2 + 6x + 5 = (x + 3)2 - 4

x2 + 8x + 5

4x2 + 8x + 1

+Practice completing the square on the following expressions:

x2 + 6x + 5 = (x + 3)2 - 4

x2 + 8x + 5 = x2 + 8x + 5 + 11 - 11

4x2 + 8x + 1

+Practice completing the square on the following expressions:

x2 + 6x + 5 = (x + 3)2 - 4

x2 + 8x + 5 = x2 + 8x + 5 + 11 – 11

= (x + 4)2 - 11

4x2 + 8x + 1

+Practice completing the square on the following expressions:

x2 + 6x + 5 = (x + 3)2 - 4

x2 + 8x + 5 = (x + 4)2 - 11

4x2 + 8x + 1

+Practice completing the square on the following expressions:

x2 + 6x + 5 = (x + 3)2 - 4

x2 + 8x + 5 = (x + 4)2 - 11

4x2 + 8x + 1 = 4x2 + 4x + 1 + 1 – 1

+Practice completing the square on the following expressions:

x2 + 6x + 5 = (x + 3)2 - 4

x2 + 8x + 5 = (x + 4)2 - 11

4x2 + 8x + 1 = 4x2 + 4x + 1 + 1 – 1

= (2x + 2)2 – 1

+Practice completing the square on the following expressions:

x2 + 6x + 5 = (x + 3)2 - 4

x2 + 8x + 5 = (x + 4)2 - 11

4x2 + 8x + 1 = (2x + 2)2 – 1

+Practice completing the square on the following expressions:

x2 + 6x + 5 = (x + 3)2 - 4

x2 + 8x + 5 = (x + 4)2 - 11

4x2 + 8x + 1 = (2x + 2)2 – 1

+What did you notice about all the problems in this lesson?

+What did you notice about all the problems in this lesson?

Everything was positive.

+On the wall wisher below, how

would this process change when given negative values in

your expression?

Be sure to put your name on your note to get credit!