Function graph x 3 3x 2. Online graphing. The stage of updating knowledge

Build a function

We bring to your attention a service for plotting function graphs online, all rights to which belong to the company Desmos. Use the left column to enter functions. You can enter manually or using the virtual keyboard at the bottom of the window. To enlarge the chart window, you can hide both the left column and the virtual keyboard.

Benefits of online charting

• Visual display of introduced functions
• Building very complex graphs
• Plotting implicitly defined graphs (e.g. ellipse x^2/9+y^2/16=1)
• The ability to save charts and get a link to them, which becomes available to everyone on the Internet
• Scale control, line color
• The ability to plot graphs by points, the use of constants
• Construction of several graphs of functions at the same time
• Plotting in polar coordinates (use r and θ(\theta))

With us it is easy to build graphs of varying complexity online. The construction is done instantly. The service is in demand for finding intersection points of functions, for displaying graphs for their further transfer to a Word document as illustrations for solving problems, for analyzing the behavioral features of function graphs. The best browser for working with charts on this page of the site is Google Chrome. When using other browsers, correct operation is not guaranteed.

The function y=x^2 is called a quadratic function. The graph of a quadratic function is a parabola. The general view of the parabola is shown in the figure below.

quadratic function

Fig 1. General view of the parabola

As can be seen from the graph, it is symmetrical about the Oy axis. The axis Oy is called the axis of symmetry of the parabola. This means that if you draw a straight line parallel to the Ox axis above this axis on the chart. Then it intersects the parabola at two points. The distance from these points to the y-axis will be the same.

The axis of symmetry divides the graph of the parabola, as it were, into two parts. These parts are called the branches of the parabola. And the point of the parabola that lies on the axis of symmetry is called the vertex of the parabola. That is, the axis of symmetry passes through the top of the parabola. The coordinates of this point are (0;0).

Basic properties of a quadratic function

1. For x=0, y=0, and y>0 for x0

2. The quadratic function reaches its minimum value at its vertex. Ymin at x=0; It should also be noted that the maximum value of the function does not exist.

3. The function decreases on the interval (-∞; 0] and increases on the interval )