The following reflections of these videos.
1. Quadratic Form
Basic quadratic form like (3x-1)(x+2) = 3x2 + 5x – 2
Standard form for:
Quadratic equal
y = ax2 + bx + c, we called it is function
Linear equation
y = mx + b
where m is not equal to 0. The domain and range the function is the set of all real numbers. The graph of linear is a line with slope m and y intercept b.
Rate of change for quadratic not constant.
Changing rate of change:
At x = 0, y = 100
x = 1, y = 84
x= 2, y = 36
We can take the simple number to replace x, e.g . 0, 1, 2, 3, ...
The graph of the equation y = x2 is a parabola.
2. Inequality
An algebraic relation showing that a quantity is greater than or less than another quantity. In other words, inequality is a statement of an order relationship greater than, less than, greater than or equal to, less than or equal to between two numbers or algebraic expressions (an expression that is unbalanced).
Supposing you and your friend were playing seesaw. If that situation is balanced, we can said that your weight and your friend’s weight are equal and if that situation is unbalanced, we conclude your weight is greater or less than your friend.
e. g.
3 < 5 (less than)
3 L 5 (make it easier to remember, L means less)
7 > 5 (greater than)
3. Graph Intersect
We know that lines which are parallel will never meet, never cross, or intersect each other, therefore any lines on the graph that are not parallel will meet each other at some point. In this situation, the lines is parallel which the other. So we can called parallel lines.
4. Do You Believe
The speaker in that video is a boy, his name is Dalton Sherman. In opening, he said, “I believed in me. Do you believed in me? Do you believe I can stand up here, fearless, and talk to all 20,000 of you?”
Because there’s the deal: He can does anything, be anything, create anything, dream anything, become anything – because they believe in him. And it rubs off on him.
Then, he asked to Dallas ISD, “Do you believe in my classmates?
Do you believe that every single one of us can graduate ready for college or the workplace? You better. Because next week, we’re all showing up in your schools – all 157,000 of us – and what we need from you is to believe that we can reach our highest potential. No matter where we come from, whether it’s sunny South Dallas, whether its Pleasant Grove, whether its Oak Cliff or North Dallas or West Dallas or wherever, you better not give up on us. No, you better not. Because, as you know, in some cases, you’re all we’ve got. 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. Don’t give up on my classmates.
Do you believe in your colleagues?
I hope so. They came to your school because they wanted to make a difference, too. Believe in them, trust them and lean on them when times get tough – and we all know, we kids can sometimes make it tough.
Am I right?
Can I get an Amen?
So, whether you’re a counselor or a librarian, a teacher assistant or work in the front office, whether you serve up meals in the cafeteria or keep the halls clean, or whether you’re a teacher or a principal, we need you!
Please, believe in your colleagues, and they’ll believe in you.
Do you believe in yourself? Do you believe that what you’re doing is shaping not just my generation, but that of my children – and my children’s children?
There’s probably easier ways to make a living, but I want to tell you, on behalf of all of the students in Dallas, we need you. We need you now more than ever. Believe in yourself.”
And finally he asked again, “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?”
At the end of his talk he said to the audience in attendance at Charles Rice Learning Center, “We need you, ladies and gentlemen. We need you to know that what you are doing is the most important job in the city today. We need you to believe in us, in your colleagues, in yourselves and in our goals.
If you don’t believe – well, I’m not going there.
I want to thank you for what you do – for me and for so many others.
Do you believe in me? Because I believe in me. And you helped me get to where I am today.
Dead Poet Society
This video told about a english teacher who taught the students with different method. He asked his students to look at thing in different way. In his perception, we must looking for ideas and attempted to seize the opportunity. We must dare to take the initiative (rebel daily routine), not stuck with the orthodox ideas to curb the freedom of the children to find his/her identity. Grab the opportunity that we have to become what we want.
6. Differential Equations
Simplify these solution to differential equation if finding
y = f(x)
Satisfies the equation for all values of x and y. Solve the dependent variable, usually y.
Integrate (just like we did in Calculus)
Let’s find the solution to differential equation:
dy/dx = 4x2
∫▒dy/dx = ∫▒〖4x〗^2
dy/dx = 4x2 (trying to get depending variable, y, all by itself)
dx (dy/dx) = (4x2)dx (dx is canceled out)
Now we can integrate
dy = 4x2dx (integrate the whole equation)
∫▒dy = ∫▒〖4x^2 dx〗
y = 4/3 x^3 + C (don’t forget to C)
Represent the infinite family of solution curves for the equation. Infinite numbers of identical curves, because infinite numbers of values for C.
7. Invers Function
In that video, a professor explained about inverse function. He used too bad method because he just wrote in the blackboard and as if explained just for himself. The following substance in his explain.
f(e.g) = 0
a. Function, we y = f(x) Vertical Line Test
We can solve y if we knew function of x
b. Function. x= g(y) Horizontal Line Test (Invertible)
We also can solve x if we knew function of y
For example:
y = 2x – 1
Solution:
2x – 1 = y
2x = y + 1
x = 1/2(y+1)
x = 1/2 y+ 1/2
Then the equation we exchange x to y and y to x. So we get y = 1/2 x+ 1/2
Lets look in the graph
x = 2x – 1
1 + x = 2x
1 = x
So, y = 2x – 1 and y = x intersect at x = 1
If reflected over the identity line, y = x, the original function becomes the red graph. The new red graph is also a straight line and passes the vertical line test for functions. The inverse relation of y = 2x - 1 is also a function.
If functions f and g are inverse functions
, A function composed with its inverse function yields the original starting value. f(x) = 2x – 1
g(x) = 1/2 x+ 1/2
f(g(x)) = 2(1/2 x+ 1/2) - 1 g(f(x) = 1/2 (2x – 1) + 1/2
= x + 1 - 1 = x - 1/2 + 1/2
= x = x
So,
g = f-1
f(g(x)) = f(f-1(x)) = x
g(f(x)) = f-1(f(x)) = x
Lets we look one more example.
y = (x-1)/(x+2)
In the x-axis its intersect is (1,0) and the y=axis its intersect is (0,-1/2).
So we can solve x for that equation with both sides multiplied by x + 2
y(x + 2) = x – 1
yx + 2y = x – 1
yx – x = -1 – 2y
x(y – 1) = -1 – 2y
x = (-1-2y)/(y-1)
Then the equation we exchange x to y and y to x. So we get y = (-1-2x)/(x-1)
So at x = 0 y = -1
at y = 0 -1 – 2x = 0
-2x = 1
x = -1/2
There is vertical asymptot at x = 1 and horizontal asymptot at y = -2.
Another example we can see that the equation y = 2x and y = log x
a. y = 2x
b. y = log x
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