The equation of a parabola is square function. There are several options of drawing up this equation. Everything depends on what parameters are presented in a statement of the problem.
Instruction
1. The parabola represents a curve which in the form reminds an arch and is the schedule of a power function. Regardless of which the parabola has characteristics, this function is even. Such function at which at all values of an argument from a range of definition at change of the sign of an argument the value does not change is called even: =f(x) Begin with f (-x) about the simplest functions: y=x^2. From its look it is possible to draw a conclusion that it increases both at positive, and at negative values of an argument x. A point in which x=0, and at the same time, y =0 is considered a function minimum point.
2. All main options of creation of this function and its equation are given below. As the first example the function of a look is considered below: f(x) =x^2+a where a - whole chislodlya to construct the schedule of this function, it is necessary to shift a function graph of f (x) on an of units. Y=x^2+3 function where along axis y shift function up on two units can be an example. If function with the opposite sign, for example y=x^2-3 is given, then its schedule is shifted down by axes y.
3. One more type of function which can set a parabola - f (x)= (x +a) ^2. In such cases the schedule, on the contrary, moves along abscissa axis (axis x) on an of units. For an example it is possible to consider functions: y= (x +4) ^2 and y=(x-4) ^2. In the first case where there is a function with a plus, the schedule is shifted on axis x to the left, and in the second case - to the right. All these cases are shown in the drawing.
4. There are also parabolic dependences of a type of y=x^4. At such cases of x=const, and y sharply increases. However, it concerns only even functions. Schedules of a parabola often are present also at physical tasks, for example, flight of a body describes the line similar to a parabola. Also the longitudinal section of a reflector of a headlight, lamp has an appearance of a parabola. Unlike a sinusoid, this schedule is acyclic and increasing.