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!