Refleksi Video

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 .