WARM UP (9/21) 1. Find the Greatest Common Factor (GCF) [something that is common/divisible between both terms]

2. Name 3 methods for solving Quadratic Equations.1. 2. 3.

GCF = ___a. 3x+3

b. 5x2-15x

c. 14x3+14x2

GCF = ___

GCF = ___

3

5x

14x2

Factoring

Quadratic Formula

Completing the Square

ALGEBRA 2H

MRS. ENGLAND

Week 5 Sept. 21-25Topics:

Factoring Quadratic Expressions & EquationsQuadratic Formula

QUADRATIC FUNCTIONS

Vocabulary:

1. Parabola: U-shaped graph of a quadratic

2. Vertex: lowest or highest point on graph of a quadratic

3. Axis of Symmetry: vertical line through the vertex

𝒚=𝒂𝒙𝟐+𝒃𝒙+𝒄 ;𝒘𝒉𝒆𝒓𝒆𝒂≠𝟎

Parent Function: y = x2

Axis of Symmetryx = 0 (y-axis)

Vertex(0,0)

7-2 FACTORING QUADRATIC EXPRESSIONS𝒂𝒙𝟐+𝒃𝒙+𝒄 ;𝒘𝒉𝒆𝒓𝒆𝒂=𝟏

Example A:

𝒙𝟐+𝟏𝟐𝒙+𝟑𝟐 a = ______b = ______c = ______

1

1232

SB pg. 108

1. Find factors of c that add to equal b

32

1 • 322 • 16

4 • 8

4 + 8 = 12

2. Write the sum of the factors as binomials. Write the factors as products.

(x +4)(x+8)

Example B:

𝟔 𝒙𝟐+𝟏𝟑𝒙 −𝟓 a = ______b = ______c = ______

𝒂𝒙𝟐+𝒃𝒙+𝒄 ;𝒘𝒉𝒆𝒓𝒆𝒂≠𝟏6

13-5

1. Find factors of a • c that add to equal bx ± 2 •

15**Note: 1 of the terms must be positive & other must be negative

-30

± 3 • 10± 5 • 6

-2x + 15x = 13x

2. Replace “bx” term in original eq. with factors 6x2 –2x + 15x -5 3. Group first 2 terms and last 2 terms.

(6x2 –2x) (+15x -5)

3. Group first 2 terms and last 2 terms.

(6x2 –2x) (+15x -5)

4. Pull out Greatest Common Factor (GCF) of each group.2x(3x -1) +5 (3x-1)

5. Group outside terms and inside terms. These are your FACTORS.

FACTORS: (2x+5) (3x-1)

**Note: There will always be a common group in this step. Ex. (3x-1)

PRACTICE Factor the expressions where a = 1:

Factor the expressions where a ≠ 1:

ADDITIONAL RESOURCE

Factoring Quadratic Equations:

When a = 1 : https://www.youtube.com/watch?v=yfiMho1_t4k

When a ≠1 : https://www.youtube.com/watch?v=VZBB17HJ7XU

7-3 SOLVING QUADRATIC EQUATIONS BY FACTORING

1. Set equation = 0

2. Factor like we did in 7-2 and set each binomial = 0.

3. Solve for x. These are the solutions/x-intercepts (where graph crosses x-axis).

𝒚=𝒂𝒙𝟐+𝒃𝒙+𝒄 ;𝒘𝒉𝒆𝒓𝒆𝒂≠𝟎

→𝒂𝒙𝟐+𝒃𝒙+𝒄=𝟎

PRACTICE CONTINUED… Factor the expressions where a = 1:

Factor the expressions where a ≠ 1:

HOMEWORK PRACTICE SB pg. 115 Lesson 7-3 Practice 11-19

Solutions #24-46 even; solve for zeros 26. 28. 30. 32. 34. 36.

38. 40. 42. 44. 46.

BELL WORK 9/24 Simplify:

1.

2.

3.

4.

5.

Hints:

8-1 COMPLEX/IMAGINARY NUMBERS

Example 1: Simplify radicals

What if…

Example 2: Simplify radicals

What if…

SB pg. 123Try These A

BELL WORK EXPANDED 9/24

Simplify:

1.

2.

3.

4.

5.

Hints:

METHODS FOR FINDING ZEROS OF QUADRATIC EQUATIONS

1. Factoring

2. Quadratic Formula

3. Completing the Square

9-2 QUADRATIC FORMULA•Another method for solving/finding zeros/x-intercepts of quadratic equations.

𝑥=−𝑏±√𝑏2−4𝑎𝑐2𝑎

0

Step 1: Identify a, b, & c.Step 2: Plug values into quadratic formula. Step 3: Solve for x.

Practice: Quadratic Formula

Solutions: 84. x = -1085. x = 3, 086. x = 5, -187. x = 888. x = ½ , 4

HOMEWORK Activity Practice Lesson 8-1 SB pg. 135 #1-6