Mod4 Lesson 11.notebook
February 03, 2016
Lesson 11 Completing the Square
Day 1
Objectives:
To rewrite quadratic expressions given in standard form,
2
ax + bx + c (a = 1), in the equivalent completed-square form,
2
a(x - h) + k, and recognize cases for which factored or
completed-square form is most efficient to use
Generalized Pattern:
(x + A)2 = x2 + 2Ax + A2
I remember
this!
You can use this pattern to
ALL OF YOU!
square any binomial of the form (x + A)2.
Mod4 Lesson 11.notebook
February 03, 2016
Rewrite the following perfect square quadratic expressions in standard form. Look for patterns in the coefficients, and write two sentences describing what you notice. Now try working backwards. Rewrite the following standard form quadratic expressions as perfect squares. Mod4 Lesson 11.notebook
February 03, 2016
What is different about x2 + 8x + 3?
Not a perfect square trinomial
Why is it impossible to factor this expression
as a perfect square binomial?
3 is not a perfect square
If you could change something about the last
expression to make it a perfect square, what
would you change?
ADD 13 to get 16
2
Find an expression equivalent to x + 8x + 3
that includes a perfect square binomial.
2
x + 8x + 3
Take half of 8 and square it.
2
8
= 4, 4 = 16
2
2
2
So, we need x + 8x + 16 instead of x + 8x + 3...
We need to add 13 to the expression,
but that would change the value!
Mod4 Lesson 11.notebook
February 03, 2016
We need to balance the expression:
2
x + 8x + 3
2
x + 8x + 3 + 16 - 16
2
x + 8x + + 16 + 3 - 16
2
(x + 8x + 16) - 13
(x + 4)2 - 13
2
x + 10x - 9
2
x + 10x -9 + 25 - 25
2
x + 10x + 25 (-9 - 25)
2
(x + 10x + 25) - 34
2
(x + 5) - 34
Mod4 Lesson 11.notebook
February 03, 2016
2
x - 7x + 1
2
x - 7x + 1 + 49 - 49
4
4
2
(x - 7x + 49) + 1 - 49
4
4
2
(x - 7x + 49 ) - 11.25
4
) )
x - 7
2
2
- 11.25
Rewrite each expression by completing the square.
2
1. a - 4a + 15
2
2. n - 2n - 15
2
3. c + 20c - 40
Mod4 Lesson 11.notebook
2
4. x + 6x
February 03, 2016
- 7
2
5. y - 3y + 10
2
6. k + 7k + 6
Mod4 Lesson 11.notebook
Closing
February 03, 2016
Attachments
algebra­i­m4­topic­b­lesson­11­student.docx
algebra­i­m4­topic­b­lesson­11­teacher.docx