English
Quadratic Form
Three X minus one multiplied by X
plus two equals three X square plus six X minus two. It’s also equal three X
square plus five X minus two. We can write it as below:
(3X-1)(X+2)=
3 + 6X –X- 2
= 3 + 5X – 2
, It’s the basic quadratic form.
Standart
form for quadratic equation is
y=
a + bx + c
“a,
b,and c” is constant. The Standart form
of quadratic equation is same with the Standart
form of linear equation. Let we see the equations
The
standart form of linear equations is : y= mX+c
The
standart form of quadratic equations is:
y= a+
bx+C
(a,b,c,
and m are constant)
The constant “m” in linear equation
is replaced by “b” (because both are constant), the new linear equations is y=
bx + c. The difference between
a linear equation and a quadratic equation lies in the highest rank of X. The
highest rank of X in the quadratic equation is two, and linear equations is
one.
If
a graph, linear equations
will form a straight line. The
intersection between the x axis and
y axis form 4 sections, the first quadrant, the second quadrant, third quadrant
and the fourth quadrant.
In the first quadrant is the
greater value, due to the positive x and y
are positive, etc. The rate of change for linear
equations is constant.
The
graph of quadratic equations is curve/ parabola. The rate of change for
quadratic equations is not constant.
Inequality
Inequality is an expression is unbalanced, like five
is more than three (5>3) and four is less than seven (4<7). This is
illustrated as when you're playing a seesaw. If your weight and your friends are
same, there will be a balance and forming a straight line. if your friend
suddenly jumped off the seesaw, then you will fall, because you are heavier
than the other. If there is a big bruce sitting on the other side of the
seesaw, then you can not go down, because you are smaller fallow him.
From that illustration we know that inequality is greater than and less
than. The the symbol of less than is “<”, for example, two is less than
seven (2<7). Sign “<”, if
drawn will
form the upper part
numbers
L,
for easy
recall,
remember that
”L” is the prefix
of the
word “Less than”.
L
is
Less
than.
The symbol of less than ia “>”, is greater
than, for example six is greater than two. The illustration
is if
there is
a
dinosaurous who
are
hungry and will eat its prey
then
his
mouth will open like the
shape of
"<".
Dinosaurous
will eat
a larger
meal. To facilitate the
recall,
the "<" is
greater
prey.
"<"
Is
greater
than.
Parallel
lines
Parallel
lines are two
lines
or more
if
extended, would never
intersect.
This is illustrated
as
two
runners
who
ran
in the
trajectory
of each
at the
same speed. Path is
a
straight line. The runners are not
allowed
out of their trajectory, so
they will never
collide.
Parallel line is like this:
Do
You Believe in Me?
“I believe in me.”
“Do you believe in me?”
“Do you believe there I can stand up here village
and talk to twenty thousand of you?
“Because here’s the deal: I can do anything, be anything, create
anything, dream anything, become anything – because you believe in me. And it
rubs off on me.”
In this video
there is
a child
who is a representative of the students,
urging teachers
and
everyone believed him. Because He also believe in
himself. He believe that he can do anything, be
anything, dream anything and become anything. This is the
thing
that is often said by
Prof.
Dr.
Marsigit,
MA,
that
there must be “trust”
between
teachers and students. Students
have the
potential to
develop
them,
teachers
are helping to
do it. Teachers
must trust that they will be
good
graduates and gave
a great
performance
at
school.
“Do you believe in us, that we can reach a high potential?”
“We need you to believe in Us”
“Finally, do you believe that every child in Dallas needs to be ready for college or the workplace? Do you believe that Dallas students can achieve?”
Confidence wherever needed. The students wanted people believe that each one of them will graduate and be ready to go to college or work. They will be able to reach his dream. Pupils also wish there was a sense of mutual trust between him and other friends .Although you come from the different backgrounds. students were expected confidence of teachers. they also say many thanks to the official, teachers, principals and all those who helped them. In some case You’re the ones who feed us, who wipe our tears, who hold our hands or hug us when we need it. You’re the ones who love us when sometimes it feels like no else does – and when we need it the most.
Dead
Poet Society
From the trailers for films dead poets
society, we are taught to see things from a different perspective. Not the time
again we follow the usual things that people do. This video teaches (especially
for students) to think about things that are extraordinary and creative,
although it looks ridiculous. Liberate your mind and use your imagination.
Every new thought that we produce, we must have the courage to express it. Never
mind that it's wrong or right, it will fail or succeed, just try it.
The following
are excerpts of Mr.Keating’s conversation that very interesting:
Just
when you think you know something,
you
have to look at it in another way.
Even
though it may seem silly or wrong,
you
must try! Now, when you read, don't
just
consider what the author thinks.
Consider
what you think.
Boys, you must strive to find your own
voice.
Because the longer you wait to
begin,
the less likely you are to find
it
at all. Thoreau said, "Most men lead
lives
of quiet desperation." Don't be
resigned
to that. Break out!
This was revealed through a movie scene
the dead poets society. When in the class. Keating up on the table and said,
"Everything looks different from here," and he rang the bell with his
foot. He invited all the boys to follow up on the table until the bell rings.
Solving
Differentiel Equations
Simplify
the solution of differential equation is
finding the function y=f(x). Satisfies the equation for all values of x
and y. So, solve for the dependent variable usually y. The solutions
of differential equations
is an integral of
that equation. So let us use the integral to
find the value of y. Before integrate the equation must
be changed into the form dy = (....) dx
= 4 (integrated
both)
=
= (Both sides multiplied
by dx.
Why? Because we must trying to get dependent variable , y, all be itself).
( ) dx = dx (dx
on the left side are cancelled out), we find
dy=
dx
(now we can integrate)
Integrate
the whole equation:
= The integral
of dy is just y, and thr integral of is just , so we find that:
y=
+ c (don’t
forget to add c, c is every cnstant. C is represent the infinite family of
solutions curves for the equation).
It’s the graph is show the solution of
the differentiel equation. There are the infinite number of identical curves based the solution because
the invinite number values of c.
Invers
Equation
We have the function F(r,g) =0
The function y= f(x) , if we want the
function in x equation we can write the
function like this, x= g(y)
The graph of y= is in curve form
If x is greater or same than 0, graphs only half the
picture on
the right y-axis.
so, x= g(y) is invertibel.
For example, we find an equation y= 2x –
1, lets make the graph
Graph will
intersect the x axis at y equal to 0,
ie at the point (1/2,
0). And
when x is equal to zero, then the graph will
intersect the y-axis at the point
(0. -1).If
we draw a line with equation y=x, so there are an intersection. Let us find
the point of
intersection. First we subtitute and y=x into y= 2x – 1,
the result is x=2x-1. That containing
X variable are summed,
so that we obtain
x-2x=-1, then we find that x= 1. Than subtitute x= 1 in the first equation, yes
we find that y is 1. The point of this intersection is (1,1)
After that, change the
equation from x equation to y equation
2x-1=y (write the equation two x
minus one equals tu y)
2x= y+1 (move the
negative one to
the right side so that it becomes
positive one)
x=
(y+1)
(multiply both sides by )
x= y
+ ,finally we find the y equation
,
so the invers of f(x) find
by replace x by y and y by x in that equation, like this
y= +
Let’s draw the
line of equation x= y
+ on a graph that has been created above.
Graph will
intersect the x axis at y equal to 0,
ie at the point ( , 0). And
when x is equal to zero, then the graph will
intersect the y-axis at the point
(0, -1). This line is intersect with the line that make of y=x
and y= 2x – 1.
If we named the first line f and the
third line is g, we find that:
f(x)= 2x – 1
g(x)= x
+
f(g(x))
= 2g(x) – 1 (replace g (x) with
x
+ )
f(g(x))=
2 (x
+ )-1
= x+1-1
=x
g(f(x))= + (replace f (x) with
2x
– 1)
= (2x – 1) +
= x- +
=x
An invers function
multiply with that own function is x, so we can conclude that g= ,
f(g(x))
= f((x))
= x
g(f(x))= (f(x))
= x
y=
(let’s make the line of x= 1 and x= -2)
y (x+2) = (x-1)
yx+2y = x-1
yx-x = -1-2y
(y-1)x = -1- 2y
x=
you can try continue to draw a graph, here are the steps:
First determine
the point of intersection of the x and y axis
if cx=0 , so we find that y= -1-2(0) =
-1, so the intersection to
the x axis is
(0, -1)
if cy=0, we will find that -1-2x=0
-2x=1
x=
the intersection to
the y axis is
()
It’s asyimtot y= -2, x
= 1 , so, the graph will never intersect with y= -2, x = 1 .