Quadratic function calculator. We build a graph of functions online

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On the Internet it is not difficult to find calculators for plotting a function graph, which are brought to your attention in this review.

http://www.yotx.ru/

This service can build:

ordinary graphs (like y = f(x)),
specified parametrically,
point graphs,
graphs of functions in the polar coordinate system.

This online service V one step:

Enter the function to be built

In addition to constructing a graph of the function, you will receive the result of studying the function.

Plotting function graphs:

http://matematikam.ru/calculate-online/grafik.php

You can enter manually or using the virtual keyboard at the bottom of the window. To enlarge the window with the graph, you can hide both the left column and the virtual keyboard.

Advantages of online charting:

Visual display of entered functions
Building very complex graphs
Construction of graphs specified implicitly (for example, ellipse x^2/9+y^2/16=1)
The ability to save charts and receive a link to them, which becomes available to everyone on the Internet
Control of scale, line color
Possibility of plotting graphs by points, using constants
Plotting several function graphs simultaneously
Plotting in polar coordinates (use r and θ(\theta))

The service is in demand for finding points of intersection of functions, for depicting graphs for further moving them into a Word document as illustrations when solving problems, for analysis behavioral characteristics function graphs. The optimal browser for working with charts on this website page is Google Chrome. Correct operation is not guaranteed when using other browsers.

http://graph.reshish.ru/

You can build an interactive function graph online. Thanks to this, the graph can be scaled and moved around coordinate plane, which will allow you not only to receive general idea about the construction of this graph, but also to study in more detail the behavior of the function graph in sections.

To build a graph, select the function you need (on the left) and click on it, or enter it yourself in the input field and click ‘Build’. The argument is the variable 'x'.

To set a function nth root from 'x' use the notation x^(1/n) - pay attention to the parentheses: without them, following mathematical logic, you will get (x^1)/n.

You can omit the multiplication sign in expressions with numbers: 5x, 10sin(x), 3(x-1); between brackets:(x-7)(4+x); and also between the variable and brackets: x(x-3). Expressions like xsin(x) or xx will cause an error.

Consider the priority of operations and if you are not sure which will be executed first, add extra parentheses. For example: -x^2 and (-x)^2 are not the same thing.

Keep in mind that the graph may not be drawn if it tends to infinity in 'y' quickly enough, due to the inability of the computer to infinitely approach the asymptote in 'x'. This does not mean that the graph ends and does not continue indefinitely.

Trigonometric functions use radian angle units by default.

http://easyto.me/services/graphic/

In order to build several graphs in one coordinate system, check the box “Build in one coordinate system” and build graphs of functions one by one.

The service allows you to build graphs of functions that contain options.

For this:

Enter the function with parameters and click “Build graph”
In the window that appears, choose which variable to plot against. Usually this is x.
Change the settings in the History menu. The schedule will change before your eyes.

http://allcalc.ru/node/650

The service allows you to build graphs of functions in a rectangular coordinate system on a given range of values. In one coordinate plane, you can construct several graphs of functions at once.
To plot a function graph, you need to set the graph plotting area (for variable x and function y) and enter the value of the dependence of the function on the argument. It is possible to construct several graphs at the same time; to do this, you need to separate the functions using a semicolon. The graphs will be plotted on the same coordinate plane and will differ in color for clarity.

http://function-graph.ru/

To plot a function online, you just need to enter your function in a special field and click somewhere outside it. After this, the graph of the entered function will be drawn automatically.

If you need to plot several functions at the same time, then click on the blue “Add more” button. After this, another field will open in which you will need to enter the second function. Its schedule will also be built automatically.

You can adjust the color of the graph lines by clicking on the square located to the right of the function input field. The remaining settings are located directly above the graph area. With their help, you can set the background color, the presence and color of the grid, the presence and color of the axes, as well as the presence and color of the numbering of graph segments. If necessary, you can scale the function graph using the mouse wheel or special icons in the lower right corner of the drawing area.

After plotting and entering necessary changes in settings, you can download chart using the big green "Download" button at the very bottom. You will be prompted to save the function graph as a PNG image.

“Natural logarithm” - 0.1. Natural logarithms. 4. Logarithmic darts. 0.04. 7.121.

“Power function grade 9” - U. Cubic parabola. Y = x3. 9th grade teacher Ladoshkina I.A. Y = x2. Hyperbola. 0. Y = xn, y = x-n where n is the given natural number. X. The exponent is an even natural number (2n).

“Quadratic function” - 1 Definition of a quadratic function 2 Properties of a function 3 Graphs of a function 4 Quadratic inequalities 5 Conclusion. Properties: Inequalities: Prepared by 8A class student Andrey Gerlitz. Plan: Graph: -Intervals of monotonicity for a > 0 for a< 0. Квадратичная функция. Квадратичные функции используются уже много лет.

“Quadratic function and its graph” - Solution.y=4x A(0.5:1) 1=1 A-belongs. When a=1, the formula y=ax takes the form.

“8th grade quadratic function” - 1) Construct the vertex of a parabola. Plotting a graph of a quadratic function. x. -7. Construct a graph of the function. Algebra 8th grade Teacher 496 Bovina school T.V. -1. Construction plan. 2) Construct the axis of symmetry x=-1. y.

Let us choose a rectangular coordinate system on the plane and plot the values of the argument on the abscissa axis X, and on the ordinate - the values of the function y = f(x).

Function graph y = f(x) is the set of all points whose abscissas belong to the domain of definition of the function, and the ordinates are equal to the corresponding values of the function.

In other words, the graph of the function y = f (x) is the set of all points of the plane, coordinates X, at which satisfy the relation y = f(x).

In Fig. 45 and 46 show graphs of functions y = 2x + 1 And y = x 2 - 2x.

Strictly speaking, one should distinguish between a graph of a function (the exact mathematical definition of which was given above) and a drawn curve, which always gives only a more or less accurate sketch of the graph (and even then, as a rule, not the entire graph, but only its part located in the final parts of the plane). In what follows, however, we will generally say “graph” rather than “graph sketch.”

Using a graph, you can find the value of a function at a point. Namely, if the point x = a belongs to the domain of definition of the function y = f(x), then to find the number f(a)(i.e. the function values at the point x = a) you should do this. It is necessary through the abscissa point x = a draw a straight line parallel to the axis ordinate; this line will intersect the graph of the function y = f(x) at one point; the ordinate of this point will, by virtue of the definition of the graph, be equal to f(a)(Fig. 47).

For example, for the function f(x) = x 2 - 2x using the graph (Fig. 46) we find f(-1) = 3, f(0) = 0, f(1) = -l, f(2) = 0, etc.

A function graph clearly illustrates the behavior and properties of a function. For example, from consideration of Fig. 46 it is clear that the function y = x 2 - 2x takes positive values when X< 0 and at x > 2, negative - at 0< x < 2; наименьшее значение функция y = x 2 - 2x accepts at x = 1.

To graph a function f(x) you need to find all the points of the plane, coordinates X,at which satisfy the equation y = f(x). In most cases, this is impossible to do, since there are an infinite number of such points. Therefore, the graph of the function is depicted approximately - with greater or lesser accuracy. The simplest is the method of plotting a graph using several points. It consists in the fact that the argument X give a finite number of values - say, x 1, x 2, x 3,..., x k and create a table that includes the selected function values.

The table looks like this:

Having compiled such a table, we can outline several points on the graph of the function y = f(x). Then, connecting these points with a smooth line, we get an approximate view of the graph of the function y = f(x).

It should be noted, however, that the multi-point plotting method is very unreliable. In fact, the behavior of the graph between the intended points and its behavior outside the segment between the extreme points taken remains unknown.

Example 1. To graph a function y = f(x) someone compiled a table of argument and function values:

The corresponding five points are shown in Fig. 48.

Based on the location of these points, he concluded that the graph of the function is a straight line (shown in Fig. 48 with a dotted line). Can this conclusion be considered reliable? Unless there are additional considerations to support this conclusion, it can hardly be considered reliable. reliable.

To substantiate our statement, consider the function

Calculations show that the values of this function at points -2, -1, 0, 1, 2 are exactly described by the table above. However, the graph of this function is not a straight line at all (it is shown in Fig. 49). Another example would be the function y = x + l + sinπx; its meanings are also described in the table above.

These examples show that in its “pure” form the method of plotting a graph using several points is unreliable. Therefore, to plot a graph of a given function, one usually proceeds as follows. First, we study the properties of this function, with the help of which we can build a sketch of the graph. Then, by calculating the values of the function at several points (the choice of which depends on the established properties of the function), the corresponding points of the graph are found. And finally, a curve is drawn through the constructed points using the properties of this function.

We will look at some (the simplest and most frequently used) properties of functions used to find a graph sketch later, but now we will look at some commonly used methods for constructing graphs.

Graph of the function y = |f(x)|.

It is often necessary to plot a function y = |f(x)|, where f(x) - given function. Let us remind you how this is done. A-priory absolute value numbers can be written

This means that the graph of the function y =|f(x)| can be obtained from the graph, function y = f(x) as follows: all points on the graph of the function y = f(x), whose ordinates are non-negative, should be left unchanged; further, instead of the points of the graph of the function y = f(x) having negative coordinates, you should construct the corresponding points on the graph of the function y = -f(x)(i.e. part of the graph of the function
y = f(x), which lies below the axis X, should be reflected symmetrically about the axis X).

Example 2. Graph the function y = |x|.

Let's take the graph of the function y = x(Fig. 50, a) and part of this graph at X< 0 (lying under the axis X) symmetrically reflected relative to the axis X. As a result, we get a graph of the function y = |x|(Fig. 50, b).

Example 3. Graph the function y = |x 2 - 2x|.

First, let's plot the function y = x 2 - 2x. The graph of this function is a parabola, the branches of which are directed upward, the vertex of the parabola has coordinates (1; -1), its graph intersects the x-axis at points 0 and 2. On the interval (0; 2) the function takes negative values, therefore, we will symmetrically display this part of the graph relative to the abscissa axis. Figure 51 shows the graph of the function y = |x 2 -2x|, based on the graph of the function y = x 2 - 2x

Graph of the function y = f(x) + g(x)

Consider the problem of constructing a graph of a function y = f(x) + g(x). if function graphs are given y = f(x) And y = g(x).

Note that the domain of definition of the function y = |f(x) + g(x)| is the set of all those values of x for which both functions y = f(x) and y = g(x) are defined, i.e. this domain of definition is the intersection of the domains of definition, functions f(x) and g(x).

Let the points (x 0 , y 1) And (x 0, y 2) respectively belong to the graphs of functions y = f(x) And y = g(x), i.e. y 1 = f(x 0), y 2 = g(x 0). Then the point (x0;. y1 + y2) belongs to the graph of the function y = f(x) + g(x)(for f(x 0) + g(x 0) = y 1 +y2),. and any point on the graph of the function y = f(x) + g(x) can be obtained this way. Therefore, the graph of the function y = f(x) + g(x) can be obtained from function graphs y = f(x). And y = g(x) replacing each point ( x n, y 1) function graphics y = f(x) dot (x n, y 1 + y 2), Where y 2 = g(x n), i.e. by shifting each point ( x n, y 1) function graph y = f(x) along the axis at by the amount y 1 = g(x n). In this case, only such points are considered X n for which both functions are defined y = f(x) And y = g(x).

This method of plotting a function y = f(x) + g(x) is called addition of graphs of functions y = f(x) And y = g(x)

Example 4. In the figure, a graph of the function was constructed using the method of adding graphs
y = x + sinx.

When plotting a function y = x + sinx we thought that f(x) = x, A g(x) = sinx. To plot the function graph, we select points with abscissas -1.5π, -, -0.5, 0, 0.5,, 1.5, 2. Values f(x) = x, g(x) = sinx, y = x + sinx Let's calculate at the selected points and place the results in the table.