Làm ơn giúp tớ kiểm tra bài về nhà

[dethuong_x0x]

Đây là đề bài (vẫn còn)

In a typed (double spaced) paper, describe in correct mathematical language, using well-constructed paragraphs and sentences, how linear equations in two variables differ from quadratic equations in two variables. Then describe how to graphically as well as algebraically find the x- and y-intercepts of either type of equation (or how to determine there are intercepts).
Describe how to write either type of equation, linear or quadratic, in y = f(x) notation. Be specific about the processes. For the linear functions, describe how to find the slope of the line from a given linear equation or how to estimate the slope from the graph. For the quadratic functions, describe how to graphically as well as algebraically find the vertex of the parabola.
Graph each of the following functions and solve the related equations to use as examples in your paper of the processes or concepts described.
y = 3x – 5
4x + 7y = 8
y = -4x^2 -3x + 10
-7x^2 - 8x - 11 + y = 0
y=-4x^2 + 3x - 10


Bài làm của tớ

+++Linear equations in two variables differ from quadratic equations in two variables because the exponents between the variables of the linear equation and the quadratic equation is different. For detail, the variable x of the linear equation has the power of one and the variable x of the quadratic equation has the power of one and two.

+++To determine x- and y-intercept on the rectangular coordinate system (or Cartesian plane), look for the intercepts of the graph - parabola of the quadratic equation or line of the linear equation - and the x- and y-axis. The x-intercepts are the points where the graph intercept the x-axis and the y-intercepts are the points where the graph intercept the y-axis.

+++To write either type of equation, linear or quadratic, in y = f(x) notation, isolate y variable. Then, substitute f(x) for y.
For example: x^2 - y -2x = 3 - 4x
<=> x^2 - 2x - 3 + 4x = y
<=> x^2+ 2x – 3 = y
=> f(x) =x^2 + 2x – 3

+++To find the slope of the line from a given linear equation, convert the given equation into the slope form, y= mx + b, in which m is the slope.
For example: 4x – 2y – 6 = -2x
<=>6x – 6 = 2y
<=> 3x – 6 = y
<=> y = 3x – 6
In the above equation, the slope is 3.

+++To graphically as well as algebraically find the vertex of the parabola, convert the equation into

general form, ax^2 + bx + c = 0

x-vertex = -b/2a
Then substitute x-vertex for x into the equation, and we get y-vertex.

vertex(x-vertex, y-vertex)



Thanks in advance!

[chiefsmoke]

this is merely about mathematics with less requirement on writting, where do you need help. also think writing a more succinct query is easier for you to catch help from other members.

cheers

[dethuong_x0x]

this is merely about mathematics with less requirement on writting, where do you need help. also think writing a more succinct query is easier for you to catch help from other members.

cheers

I did write it in the shortest version. Do you have any shorter version. Please give me some suggestion.

[Paddy]

Đây là đề bài (vẫn còn)

In a typed (double spaced) paper, describe in correct mathematical language, using well-constructed paragraphs and sentences, how linear equations in two variables differ from quadratic equations in two variables. Then describe how to graphically as well as algebraically find the x- and y-intercepts of either type of equation (or how to determine there are intercepts).
Describe how to write either type of equation, linear or quadratic, in y = f(x) notation. Be specific about the processes. For the linear functions, describe how to find the slope of the line from a given linear equation or how to estimate the slope from the graph. For the quadratic functions, describe how to graphically as well as algebraically find the vertex of the parabola.
Graph each of the following functions and solve the related equations to use as examples in your paper of the processes or concepts described.
y = 3x – 5
4x + 7y = 8
y = -4x^2 -3x + 10
-7x^2 - 8x - 11 + y = 0
y=-4x^2 + 3x - 10


Bài làm của tớ

+++Linear equations with two variables differ from quadratic equations in two variables because the exponents between the variables of the linear equation and the quadratic equation are different. For instance, the variable x of the linear equation has the power of one and the variable x of the quadratic equation has the power of one and two.

+++To determine x- and y-intercept on the rectangular coordinate system (or Cartesian plane), look for the intercepts of the graph - parabola of the quadratic equation or line of the linear equation - and the x- and y-axis. The x-intercepts are the points where the graph intercept the x-axis and the y-intercepts are the points where the graph intercept the y-axis.

+++To write either type of equation, linear or quadratic, in y = f(x) notation, isolate y variable. Then, substitute f(x) for y.
For example: x^2 - y -2x = 3 - 4x
<=> x^2 - 2x - 3 + 4x = y
<=> x^2+ 2x – 3 = y
=> f(x) =x^2 + 2x – 3

+++To find the slope of the line from a given linear equation, convert the given equation into the slope form, y= mx + b, in which m is the slope.
For example: 4x – 2y – 6 = -2x
<=>6x – 6 = 2y
<=> 3x – 6 = y
<=> y = 3x – 6
In the above equation, the slope is 3.

+++To graphically as well as algebraically find the vertex of the parabola, convert the equation into

general form, ax^2 + bx + c = 0

x-vertex = -b/2a
Then substitute x-vertex for x into the equation, and we get y-vertex.

vertex(x-vertex, y-vertex)



Thanks in advance!

Correction in red.

Nếu học tới hình học giải tích (Calculus with Analytic Geometry)thì nói thêm vô là slope của linear thì là constant m. Slope của quadratic eq thì là 2aX + B, tức là slope thay đổi tuỳ theo điểm X. Vertex là trường hợp đặc biệt khi slope = 0 = 2AX + B.

[dethuong_x0x]

Correction in red.

Nếu học tới hình học giải tích (Calculus with Analytic Geometry)thì nói thêm vô là slope của linear thì là constant m. Slope của quadratic eq thì là 2aX + B, tức là slope thay đổi tuỳ theo điểm X. Vertex là trường hợp đặc biệt khi slope = 0 = 2AX + B.

Thank you very much, Mr.Paddy!

[dethuong_x0x]

100% bạn này đang học bên Mỹ,^^, slope, vertex chỉ dùng ở Mỹ thui, còn ct anh , úc thì ng ta dùng gradient với lại Turning poit ^^
Hix, chỉ là ý kien gom gop thui, hok bit có đúng ko, ai rành thì confirm lại nhé

Ở mỹ cũng dùng turning point nữa

[slob_cat]

Ở mỹ cũng dùng turning point nữa

uhm, tai thay jao là đa wuoc ja mà. Giong nhu ben minh cũng có ng xài vertex. Nhung mà thay textbook thì toàn turning point thui. Gap cái đề mà có vertex voi slope chax mình bỏ jay trắng rùi á

[english-learner]

uhm, tai thay jao là đa wuoc ja mà. Giong nhu ben minh cũng có ng xài vertex. Nhung mà thay textbook thì toàn turning point thui. Gap cái đề mà có vertex voi slope chax mình bỏ jay trắng rùi á

turning point là điểm uốn (chỗ cực trị của hàm) còn vertex là đỉnh chổ hàm có cực trị hai cái này khác nghĩa nhau.

[english-learner]

Đây là đề bài (vẫn còn)

In a typed (double spaced) paper, describe in correct mathematical language, using well-constructed paragraphs and sentences, how linear equations in two variables differ from quadratic equations in two variables. Then describe how to graphically as well as algebraically find the x- and y-intercepts of either type of equation (or how to determine there are intercepts).
Describe how to write either type of equation, linear or quadratic, in y = f(x) notation. Be specific about the processes. For the linear functions, describe how to find the slope of the line from a given linear equation or how to estimate the slope from the graph. For the quadratic functions, describe how to graphically as well as algebraically find the vertex of the parabola.
Graph each of the following functions and solve the related equations to use as examples in your paper of the processes or concepts described.
y = 3x – 5
4x + 7y = 8
y = -4x^2 -3x + 10
-7x^2 - 8x - 11 + y = 0
y=-4x^2 + 3x - 10


Bài làm của tớ

+++Linear equations in two variables differ from quadratic equations in two variables because the exponents between the variables of the linear equation and the quadratic equation is different. For detail, the variable x of the linear equation has the power of one and the variable x of the quadratic equation has the power of one and two.

+++To determine x- and y-intercept intersection (?) on the rectangular coordinate system (or Cartesian plane), look for the intercepts/intersection of the graph - parabola of the quadratic equation or line of the linear equation - and the x- and y-axis. The x-interceptsintersection are the points where the graph intercept the x-axis and the y-intercepts are the points where the graph intercept the y-axis.

+++To write either type of equation, linear or quadratic, in y = f(x) notation, isolate y variable. Then, substitute f(x) for y.
For example: x^2 - y -2x = 3 - 4x
<=> x^2 - 2x - 3 + 4x = y
<=> x^2+ 2x – 3 = y
=> f(x) =x^2 + 2x – 3

+++To find the slope of the line from a given linear equation, convert the given equation into the slope form, y= mx + b, in which m is the slope.
For example: 4x – 2y – 6 = -2x
<=>6x – 6 = 2y
<=> 3x – 6 = y
<=> y = 3x – 6
In the above equation, the slope is 3.

+++To graphically as well as algebraically find the vertex of the parabola, convert the equation into

general form, ax^2 + bx + c = 0

x-vertex = -b/2a
Then substitute x-vertex for x into the equation, and we get y-vertex.

vertex(x-vertex, y-vertex)



Thanks in advance!

Học ở Mỹ thì dùng slope ở các nước nói tiếng Anh khác thì dùng gradient, ngoài ra còn có inclination tính ra độ (không để dạng hữu tỉ)
Intercept là chắn, chặn (chẳng hạn như góc nội tiếp chắn cung ở đường tròn) còn intersection là sự giao nhau, giao điểm==>intersect (v)