1. Minds On : Factor completely: 4x 2 - 4x +1= 3x 2 +6x+9 = Determine the value of k that makes the expression a perfect square trinomial: x 2 - 12x +k =

2. Review: Factoring, Quadratic formula, Axis of symmetry, Radicals

3. Factor the expression x 2 - 2x - 3 = ( )( ) The product of the last terms must be ________ We have many options, to have a product of _______ Find the combination that will yield the correct "middle term" of -2x

4. Difference of squares (x - 3)(x + 3) = x 2 – 9 ( x + 5)(x – 5) = x 2 – 25 9x 2 – 4 = ( 3x -2 )(3x + 2 )

5. Factor the expressions: 2x 2 - 6x - 8 = 2( x 2 - 3x – 4 ) = 2( x – 4 )( x +1 )

6. Expand and identify the pattern ( x + 5 ) 2 = ( x + 5 ) ( x + 5 ) = x 2 + 10x + 25 = (1x) 2 +(2)(1)(5) + (5) 2

7. Factor x 2 - 6x + 9 = ( x – 3 ) 2 x 2 +12x + 36 = ( x – 6 ) 2

8. 2x 2 + x – 6 = ( ) ( ) Multiply ac (2)(-6) = Possible factors of – 12 : Find the combination that will yield the correct "middle term" of +x Practice 1) Factor the trinomial ( decomposition) (a ≠ 1)

9. # 1 Answers: 2x 2 + x – 6 = ( ) ( ) ax 2 + b x + c Multiply ac (2)(-6) = -12 Possible factors of - 12: - 6 and + 2 +6 and - 2 -3 and +4 - 3x and 4x 12 and - 1 - 12 and +1 Find the combination that will yield the correct "middle term" of +x 3 and - 4

10. Re-write the middle term, forming two terms, using these two values (order is not important): 2x 2 - 3x + 4x – 6 Group the first two terms together and group the last two terms together. Notice the plus sign between the two groups. (2x 2 -3x) + (4x - 6) # 1) 2x 2 + x – 6 = ( ) ( )

11. # 1 Answers Continued: Factor the greatest common factor out of each group.. x(2x -3) + 2(2x – 3) Notice that the expressions in the parentheses are identical. By factoring out the parentheses binomial: 2x 2 + x – 6 = (2x - 3)(x +2)

12. ac Middle term’s coefficient Practice # 2) : Factor the trinomial (Box Method) 3x 2 - 5x - 2 = ( x - 2 ) ( 3x + 1)

13. Find the roots by using the Quadratic Formula y = -2x² + 8x – 1 is called discriminant

14. Connect the number of zeros to the Quadratic Formula: We can use the discriminant to tell us whether or not a quadratic function has 1, 2 or no zeros without solving for the zeros

15. If b² - 4ac is > 0... there are 2 zeros If b² - 4ac is = 0... there is 1 zero If b² - 4ac is < 0... there are no zeros

16. If b² - 4ac is > 0... there are 2 zeros Ex. y = -2x² + 8x – 1 a = -2, b = 8, c = -1 b² - 4ac (discriminant) = 8² - 4(-2)(-1) = 64 – 8 = 56 > 0... there are 2 zeros

17. y = - 2x² + 8x – 1 Zeros: x=0 and x=4 Axes of symmetry: = sum of the zeros divided by 2 Therefore x = - b/(2a)

18. Complete the square Write f(x) = x 2 + 4x + 3 in vertex form.

19. Factor the coefficient of x 2 for the first two terms Add and subtract half of the coefficient of the x term squared Remove the fourth term Factor the perfect square and simplify The vertex is (- 2, -1) Example 1: Put in vertex form. f(x) = x 2 + 4x + 3 f(x) =1 (x 2 + 4x) + 3 f(x) = 1(x 2 + 4x + 2 2 - 2 2 ) + 3 f(x) =1 (x 2 + 4x + 2 2 ) - 2 2 + 3 f(x) = 1(x 2 + 4x + 2 2 - 2 2 ) + 3 f(x) =1 (x + 2 ) 2 - 1

20. Radicals page 35-40 Examples from the textbook

21. Practice/ Homework: Page 39: # 1-4(a,c,f) 5-7(b,d,e)