How to write the equation of a parabola

Parabola is a curve that resembles the arc is the graph of the exponential function. Regardless of what features of the parabola, this function is even. Even called such a function which for all values of the argument out of scope when you change the sign of the argument value is not changed:f(-x)=f(x)Starting with the most simple functions: y=x^2. Of its kind it can be concluded that it increases both positive and negative values of the argument x. The point at which x=0, and thus y =0 is a minimum point of the function.

Below are all the basic options for constructing this function and its equation. As the first example below considers the function of the form:f(x)=x^2+a, where a is an integer of cyclods in order to graph this function, you must move the graph of the function f(x) on a units. An example is the function y=x^2+3, where along the y axis, move the function up by two units. If given a function with the opposite sign, for example y=x^2-3, then its graph move down on the y-axis.

Another type of function which can be set parabola - f(x)=(x +a)^2. In such cases, the timing, on the contrary, moves along the x-axis (x-axis) on a units. For example, consider the function: y=(x +4)^2 and y=(x-4)^2. In the first case, where there is a function with a plus sign, shift the graph along the x-axis to the left, and in the second case to the right. All these cases shown in the figure.

There are also parabolic dependence of the form y=x^4. In such cases, x=const, and y increases dramatically. However, this applies only to even functions.Graphs of the parabola and are often present in physical problems, for example, the flight of the body describes a line that is similar to a parabola. It is also a kind of a parabola is a longitudinal section of a reflector of a headlamp, a flashlight. Unlike sine waves, this schedule is non-periodic and increasing.