Quadratic and cubic functions

The function y=x^2 is called a quadratic function. Schedule quadratic function is a parabola. General form 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 Oy axis is called the axis of symmetry of the parabola. This means that if you draw a straight line on the graph parallel to the Ox axis above this axis. Then it will intersect 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 a parabola into two parts. These parts are called branches of the parabola. And the point of a parabola that lies on the axis of symmetry is called the vertex of the parabola. That is, the axis of symmetry passes through the vertex of the parabola. The coordinates of this point are (0;0).

Basic properties of a quadratic function

1. At x =0, y=0, and y>0 at x0

2. Minimum value the quadratic function reaches its vertex. Ymin at x=0; It should also be noted that the function does not have a maximum value.

3. The function decreases on the interval (-∞;0] and increases on the interval , because the straight line y=kx will coincide with the graph y=|x-3|-|x+3| in this section. This option is not suitable for us.

If k is less than -2, then the straight line y=kx with the graph y=|x-3|-|x+3| will have one intersection. This option suits us.

If k=0, then the intersection of the straight line y=kx with the graph y=|x-3|-|x+3| there will also be one. This option suits us.

Answer: for k belonging to the interval (-∞;-2)U)