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