Today:Warm-Up: Review for Final

ExamSolving Quadratic

Equations by Completing the Square

Class Work

April 12, 2013

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.

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 - 5Term

sIs it a

Monomial?

3. Write 3 actual monomials

Warm-Up/Final Exam Review:

Adding, Subtracting Polynomials

What is the degree of the resulting polynomial?

What is the degree of the resulting polynomial?

Warm-Up/Final Exam Review:

Solving Quadratic Equations by Completing the Square:

1. So far, we have learned three different methods for solving quadratic equations. Name them.

Solving Quadratic Equations by Completing the Square:

By factoring, By Graphing, and by Square RootsToday 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

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.

Example 1: x2 + 6x - 2 = 0

x2 + 6x = 2

x2 + 6x + 9 = 2 + 9

(x + 3) 2 = 11

x + 3 = ± √11; x = -3 ± √11

Example 2: x2 + 8x + 4 = 0

x2 + 8x = - 4

x2 + 8x + 16 = - 4 + 16

(x + 4) 2 = 12

x + 4 = ± 2√3; x = -4 ± 2√3

Example 3: x2 - 10x + 20 = 0

x = 5 ± √5

where.... and....

Another Way to View the Process....

Example 2: x2 + 8x + 4 = 0

d = 8/2 = 4 and e = 4 - (64/4) 16 = -

12Therefore, (x + 4)2 - 12 = 0; = (x + 4)2 = 12

x + 4 = ± 2√3; x = -4 ± 2√3

Solving Quadratic Equations by Completing the Square:

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.

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.

Class Work

Completing the Square Handout:

Work with a partner if you like

#'s: 4-18

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

where.... and....