The parabola is the schedule of square function of a type of y=A·x \· x+C. Before creation of the schedule it is necessary to conduct an analytical research of function. Usually the parabola is drawn in the Cartesian rectangular system of coordinates which is presented by two perpendicular axes of Ox and Oy.

## Instruction

1. The first point write down a range of definition of function D (y). The parabola is defined on all numerical straight line if no additional conditions are set. Usually it is specified by record D (y) = R where R is a set of all real numbers.

2. Find **parabola** top. Coordinate on x0=-B/2A abscissa axis. Substitute x0 in the equation of a parabola and count top coordinate on Oy ordinate axis. So, the second point has to record will appear: (x0; y0) – parabola top coordinates. Naturally, instead of x0 and y0 you have to have concrete numbers. Note this point on the drawing.

3. Comparing the senior coefficient of A at x² to zero, draw a conclusion on the direction of branches of a parabola. If A> 0, then branches of a parabola are directed up. At negative value of number A of a branch of a parabola are directed down.

4. Now you can find a set of values of the E(y) function. If branches are directed up, function y accepts all values above of y0. At the direction of branches down function accepts values below of y0. For the first case write down: E(y)= [y0,+ ∞), for the second – E(y)= (-∞; y0]. The square bracket says that the extreme number joins in an interval.

5. Write the equation for an axis of symmetry of a parabola. It will have an appearance: and to pass x=x0 through top. Draw this axis strictly perpendicular to Ox axis.

6. Find "zero" function. These points will cross coordinate axes. Equate also to zero and count y for this case. Then find at what values of an argument function y will address in zero. For this purpose solve quadratic equation A·x \· x+C=0. Note points on graphics.

7. Find additional points for creation of a parabola. Issue in the form of the table. In the first line write down an argument x, the second – function y. It is better to select such numbers for which x and y will be whole since it is inconvenient to represent fractional numbers. Note the received points on graphics.