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 is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
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Similar to 3_1 Exponential functions and their graphs (1).ppt
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 is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
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.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
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The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
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Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
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2. 2
The exponential function f with base b is
defined by
f(x) = abx
where b > 0, b 1, and x is any real number.
** when b> 1; b is considered a growth factor.
For instance,
f(x) = 3x and g(x) = 0.5x
are exponential functions.
3. 3
The value of f(x) = 3x when x = 2 is
f(2) = 32 =
The value of g(x) = 0.5x when x = 4 is
g(4) = 0.54 =
The value of f(x) = 3x when x = –2 is
9
1
9
f(–2) = 3–2 =
0.0625
4. 4
The graph of f(x) = abx, b > 1
y
x
(0, 1)
Domain: (–, )
Range: (0, )
Horizontal Asymptote
y = 0
4
4
5. 5
The graph of f(x) = abx, 0 < b < 1
y
x
(0, 1)
Domain: (–, )
Range: (0, )
Horizontal Asymptote
y = 0
4
4
Since a< 1;
a is decay
factor.
6. 6
Example: Sketch the graph of f(x) = 2x.
x
y
2
–2
2
4
x f(x)
-2
-1
0
1
2
2-2 = 1/4
2-1 = 1/2
20 = 1
21 = 2
22 = 4
7. 7
Example: Sketch the graph of g(x) = 2x – 1. State the
domain and range.
x
y
The graph of this
function is a vertical
translation of the
graph of f(x) = 2x
down one unit .
f(x) = 2x
y = –1
Domain: (–, )
Range: (–1, )
2
4
8. 8
Example: Sketch the graph of g(x) = 2-x. State the
domain and range.
x
y
The graph of this
function is a
reflection the graph
of f(x) = 2x in the y-
axis.
f(x) = 2x
Domain: (–, )
Range: (0, ) 2
–2
4
9. 9
Example: Sketch the graph of g(x) = 4x-3 + 3.
State the domain and range.
x
y
Make a table.
Domain: (–, )
Range: (3, ) or y > 3
2
–2
4
x y
3 4
2 3.25
1 3.0625
4 7
5 19
10. 10
Write an exponential function y = abx for the
graph that includes the given points.
(2, 2) and (3, 4)
y = abx Substitute in (2,2) for x and y.
2 = ab2
Solve for a
2 = a
b2
Now substitute (3,4) in for x and y into y = abx
4 = ab3
b3
4 = a
b3
Set them equal to each other:
2 = 4 = a
b3 b2
Now solve for b to get b=2
You must solve for a: 2/2^2 = (1/2) = a
Subst you’re a = (1/2) & b = 2 into either one
of your 2 equations: y = abx
Y = (1/2)(2)^x
11. 11
Write an exponential function y = abx for the
graph that includes the given points.
(2, 4) and (3, 16)
y = abx
12. 12
The irrational number e, where
e 2.718281828…
is used in applications involving growth and
decay.
Using techniques of calculus, it can be shown
that
n
e
n
n
as
1
1
The Natural Base e
13. 13
The graph of f(x) = ex
y
x
2
–2
2
4
6
x f(x)
-2 0.14
-1 0.38
0 1
1 2.72
2 7.39
14. 14
Example: Sketch the graph of g(x) = ex-5 + 2.
State the domain and range.
x
y
Make a table.
Domain: (–, )
Range: (2, ) or y > 2
2
–2
4
x y
5 3
6 4.72
7 9.39
4 2.36
3 2.14
16. 16
Formulas for Compound Interest—
1.) compound per year -- A = P 1 + r nt
n
Interest Applications
Balance in account Principal ($ you invest)
r is the rate
n is the number times you
compound your money per
year
t is time.
2. Compounded continuously– A = Pert
17. 17
A total of $12000 is invested at an annual
interest rate of 9%. Find the balance after
5 years if it is compounded
a. quarterly
b. monthly
c. continuously
