Good Morning !
So on Friday morning we covered a lot of different things, we reviewed our quizzes, revisited topics we have already learned as well as learning new things !

We started with looking at question # 1 on the "Quadratic Functions Complete the Square Pattern Activity"
Mr P. explained to us why (x+3)² ≠ x² + 9 . He also explained how it all leads back to algebra tiles...
(x+1)² = x² + 2x + 1  or  (x + 1)² = (x + 1)(x + 1)
This web site allows you to play around with the algebra tiles (:

http://nlvm.usu.edu/en/nav/frames_asid_189_g_4_t_2.html?open=activities&from=category_g_4_t_2.html

We discovered a pattern ...
ex.
(x+3)² = x² + 6x + 9           If you take the b variable (6) and divide it by 2 and then square it becomes the
(6/2)² = 9                           c variable (9)

ex.
x² + 8x + 16
(8/2)² = 16

We looked over the Complete the Square Worksheet, Mr P. explained three questions .

1. a² + 16a + c   (16/2)²  = 64   c = 64
2. n² - 17n + c    (-17/2)² = 289/4 c=
3. y² - 4/5y + c   (-4/5/2)² = (4/3 . 1/2) = (-4/10)²  reduces to (-2/5)² = 4/25   c= 4/25

We Finished Class by learning two methods to complete the square .

Mr P's Favourite (Method One)
                                                                                  
y= x² + 6x + 8                                                            Steps
                                                 1. Equate it all to zero
x² + 6x + 8 = 0
                                                2. Move c variable (8) to right hand side don't forget to change the sign !
x² + 6x = -8
                                                3. We want to Complete the Square . Divide b variable by 2 then square
(6/2)² = 9                                      it to equal c variable.

x² + 6x + 9 = -8 + 9                  *What ever you do for the left side you must also do for the right.
                                                     make it equal out . *
x² + 6x + 9 = 1                         4. So we add 9 to both sides
                                                    * perfect square means it factors nicely *
(6/2)² = 9 6/2 = 3 = (x + 3)² = 1      Use value in bracket to factor (6/2 = 3)
                                                5. Equate it all to zero again

(x + 3)² - 1 = 0                         6. Change back to vertex (standard) form
y = (x + 3)² - 1                                                            FINISHED (:

                                 OR .

( Method Two. )rm
- using example one from the book.

y = x² - 2x + 3                                      Take half of the middle term add to this equations subtract,
                                                             factor trinomial into a binomial
(-2/2)² = 1
                                                            * Must subtract 1 because nothing is being moved *
y= ( x² - 2x + 1) + 3 - 1
                    
y= (x-1)² + 2

H O M E W O R K

Complete the Square "Value of c worksheet"
Complete the Square Worksheet 2
Exercise Book ; Examples pg. 26,27,28 and Exercise 4 questions 1,2,9 and 10 .

If you don't understand Mr P gave the option of leaving out pg 27 ex. 3,4,5,6 for Monday .

Hope you guys had a great long weekend see you in class on Monday ! (:

- KristynOrvis .