1. April 12, 2013 Today:
Warm-Up: Review for Final Exam
Solving Quadratic Equations by
Completing the Square
Class Work

2. Reminders:
•Khan Academy Topics for Sunday
•Final Exam Tuesday
•At theV6Math site:
•Lots of practice questions, unit quizzes, study guides
and every class day's activities for download.

3. Warm-Up/Final Exam Review:
Poly Questions about Polynomials
1. Name two Polynomial sub sets: Monomials, Binomials
2. The suffix 'nomial' means what?3x, 3x + 2, 3x2 + 2x - 5
Terms Is it a Monomial?
3. Write 3 actual monomials

4. Warm-Up/Final Exam Review:
Adding, Subtracting Polynomials
What is the degree of the
resulting polynomial?
What is the degree of the
resulting polynomial?

5. Warm-Up/Final Exam Review:

6. Solving Quadratic Equations by
Completing the Square:

8. Solving Quadratic Equations by
Completing the Square:
1. So far, we have learned three different methods for
solving quadratic equations. Name them.
By factoring, By Graphing, and by Square Roots
Today we're going to learn a 4th way to solve quadratic
equations. We're adding a too to our toolbox for those
times when it's needed.
Can we solve x2 + 8x + 7? Yes No Maybe (x + 7)(x + 1)
Can we solve 8x2 - 22x + 12? Yes No Maybe
What about 48x2 + 22x - 15? Yes No Maybe

9. Solving Quadratic Equations by
Completing the Square:
So there are times when we could use that extra tool to
solve certain quadratic equations. This method is called
completing the Square.
Completing the square takes a trinomial that is not a
perfect square, and turns it into a perfect square
trinomial by adding the correct constant term.

10. x Example 1: x2=+-3 ±-√11 0
+ 3 = ± √11; 6x 2 =
x2 + 6x = 2
x2 + 6x + 9 = 2 + 9
(x + 3) 2 = 11

11. x + 4 = ± 2√3; x 2 + 8x + 4 = 0
Example 2: x = -4 ± 2√3
x2 + 8x = - 4
x2 + 8x + 16 = - 4 + 16
(x + 4) 2 = 12

12. Example 3: x2 - 10x + 20 = 0
x = 5 ± √5

13. Another Way to View the Process....
where.... and....
Example 2: x2 + 8x + 4 = 0 d = 8/2 = 4 and
e = 4 - (64/4) 16 = -12
Therefore, (x + 4)2 - 12 = 0; = (x + 4)2 = 12
x + 4 = ± 2√3; x = -4 ± 2√3

14. Solving Quadratic Equations by
Completing the Square:
There are only slight differences between the two
methods and both yield the same result. Try them both
until you are comfortable with one. In either case, you
must memorize the steps involved. As usual, focus not
on the math, but on the process.
Right now we are only going to work on equations
where the 'a' coefficient is 1. Monday we will work with
those equations whose coefficients are > 1.

15. Class Work
Completing the Square Handout:
Work with a partner if you like
#'s: 4-18

16. x²+6x -30
x²+4x-8
x²+16x-27
x²-10x-36
x²-3x-9

20. where.... and....