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+
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!