Build a graph for x2. Quadratic and Cubic Functions. Homework

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 you can see 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. Then it will cross the parabola at two points. The distance from these points to the Oy axis will be the same.

The axis of symmetry divides the graph of the parabola into two parts, as it were. 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 apex of the parabola. The coordinates of this point (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 function does not have a maximum value.

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