Building charts online. Plotting online Basic properties of a quadratic function

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 )