This learner's module discusses or talks about the topic of Quadratic Functions. It also discusses what is Quadratic Functions. It also shows how to transform or rewrite the equation f(x)=ax2 + bx + c to f(x)= a(x-h)2 + k. It will also show the different characteristics of Quadratic Functions.
This will help you in factoring sum and difference of two cubes.
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This powerpoint presentation discusses or talks about the topic or lesson Functions. It also discusses and explains the rules, steps and examples of Quadratic Functions.
This learner's module discusses or talks about the topic of Quadratic Functions. It also discusses what is Quadratic Functions. It also shows how to transform or rewrite the equation f(x)=ax2 + bx + c to f(x)= a(x-h)2 + k. It will also show the different characteristics of Quadratic Functions.
This will help you in factoring sum and difference of two cubes.
For more instructional resources, CLICK me here!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
This powerpoint presentation discusses or talks about the topic or lesson Functions. It also discusses and explains the rules, steps and examples of Quadratic Functions.
I have added to the original presentation in response to one of the comments.... the result of 'x' is correct on slide 7, take a look at the new version of this ppt to clear up any confusion about why...
I have added to the original presentation in response to one of the comments.... the result of 'x' is correct on slide 7, take a look at the new version of this ppt to clear up any confusion about why...
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This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
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In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
3. Holt Algebra 1
7-8 Special Products of Binomials
Find special products of binomials.
Objective
4. Holt Algebra 1
7-8 Special Products of Binomials
Vocabulary
perfect-square trinomial
difference of two squares
5. Holt Algebra 1
7-8 Special Products of Binomials
Imagine a square with sides of length (a + b):
The area of this square is (a + b)(a + b) or (a + b)2.
The area of this square can also be found by adding the
areas of the smaller squares and the rectangles inside.
The sum of the areas inside is a2 + ab + ab + b2.
6. Holt Algebra 1
7-8 Special Products of Binomials
This means that (a + b)2 = a2+ 2ab + b2.
You can use the FOIL method to verify this:
(a + b)2 = (a + b)(a + b) = a2 + ab + ab + b2
F L
I
O = a2 + 2ab + b2
A trinomial of the form a2 + 2ab + b2 is called a
perfect-square trinomial. A perfect-square
trinomial is a trinomial that is the result of
squaring a binomial.
7. Holt Algebra 1
7-8 Special Products of Binomials
Multiply.
Example 1: Finding Products in the Form (a + b)2
A. (x +3)2
(a + b)2 = a2 + 2ab + b2
Use the rule for (a + b)2.
(x + 3)2 = x2 + 2(x)(3) + 32
= x2 + 6x + 9
Identify a and b: a = x and
b = 3.
Simplify.
B. (4s + 3t)2
8. Holt Algebra 1
7-8 Special Products of Binomials
Multiply.
Example 1C: Finding Products in the Form (a + b)2
C. (5 + m2)2
9. Holt Algebra 1
7-8 Special Products of Binomials
Check It Out! Example 1
Multiply.
A. (x + 6)2
B. (5a + b)2
10. Holt Algebra 1
7-8 Special Products of Binomials
Check It Out! Example 1C
Multiply.
(1 + c3)2
11. Holt Algebra 1
7-8 Special Products of Binomials
You can use the FOIL method to find products in
the form of (a – b)2.
(a – b)2 = (a – b)(a – b) = a2 – ab – ab + b2
F L
I
O = a2 – 2ab + b2
A trinomial of the form a2 – 2ab + b2 is also a
perfect-square trinomial because it is the result
of squaring the binomial (a – b).
12. Holt Algebra 1
7-8 Special Products of Binomials
Multiply.
Example 2: Finding Products in the Form (a – b)2
A. (x – 6)2
(a – b) = a2 – 2ab + b2
(x – 6) = x2 – 2x(6) + (6)2
= x – 12x + 36
Use the rule for (a – b)2.
Identify a and b: a = x and
b = 6.
Simplify.
B. (4m – 10)2
13. Holt Algebra 1
7-8 Special Products of Binomials
Multiply.
Example 2: Finding Products in the Form (a – b)2
C. (2x – 5y )2
D. (7 – r3)2
14. Holt Algebra 1
7-8 Special Products of Binomials
Check It Out! Example 2
Multiply.
a. (x – 7)2
b. (3b – 2c)2
15. Holt Algebra 1
7-8 Special Products of Binomials
Check It Out! Example 2c
Multiply.
(a2 – 4)2
16. Holt Algebra 1
7-8 Special Products of Binomials
(a + b)(a – b) = a2 – b2
A binomial of the form a2 – b2 is called a
difference of two squares.
17. Holt Algebra 1
7-8 Special Products of Binomials
Multiply.
Example 3: Finding Products in the Form (a + b)(a – b)
A. (x + 4)(x – 4)
(a + b)(a – b) = a2 – b2
(x + 4)(x – 4) = x2 – 42
= x2 – 16
Use the rule for (a + b)(a – b).
Identify a and b: a = x
and b = 4.
Simplify.
B. (p2 + 8q)(p2 – 8q)
18. Holt Algebra 1
7-8 Special Products of Binomials
Multiply.
Example 3: Finding Products in the Form (a + b)(a – b)
C. (10 + b)(10 – b)
19. Holt Algebra 1
7-8 Special Products of Binomials
Check It Out! Example 3
Multiply.
a. (x + 8)(x – 8)
b. (3 + 2y2)(3 – 2y2)
20. Holt Algebra 1
7-8 Special Products of Binomials
Check It Out! Example 3
Multiply.
c. (9 + r)(9 – r)
21. Holt Algebra 1
7-8 Special Products of Binomials
Write a polynomial that represents the
area of the yard around the pool
shown below.
Example 4: Problem-Solving Application
22. Holt Algebra 1
7-8 Special Products of Binomials
Check It Out! Example 4
Write an expression that represents
the area of the swimming pool.