The parabola is a flat curve of the second order which initial equation in the Cartesian system of coordinates has y appearance²=2px. Where r is the focal parameter of a parabola equal to distance from the fixed point of F called focus to the fixed straight line of D in the same plane bearing a name – the head mistress. The top of such parabola passes through the beginning of coordinates, and the curve is symmetric concerning abscissa axis Oh. In a school course of algebra it is accepted to consider a parabola which axis of symmetry coincides with ordinate axis of Ou: x \. And the equation at the same time registers a little differently: y=ax²+bx+c, and =1 / (2p). It is possible to draw a parabola in several ways, conditionally which it is possible to call algebraic and geometrical.
Instruction
1. Algebraic creation of a parabola. Find out coordinatestopsparabola . Oh calculate coordinate on an axis on a formula: x0=-b / (2a), and on axis Oy: / 4a or substitute y0=-(b²-4ac) the received value h0 in y0=ax0 parabola equation²+bx0+c and calculate value.
2. On the coordinate plane construct an axis of symmetry of a parabola. Its formula coincides with a coordinate formula h0 parabola tops: x=-b / (2a). Define where parabola branches are directed. If a> 0, axes are directed up if and
3. Take randomly 2-3 values for parameter x so that: h0
4. Put the end 1', 2', and 3' so that they were symmetric to points 1, 2, 3 concerning a symmetry axis.
5. Connect points 1', 2', 3', 0, 1, 2, 3 smooth curve. Continue the line up or down, depending on the direction of a parabola. The parabola is constructed.
6. Geometrical creation of a parabola. This method is based on definition of a parabola as sets of the points equidistanted both from F focus and from the head mistress of D.Poetomu at first find the focal parameter of the set parabola r =1 / (2a).
7. Construct an axis of symmetry of a parabola as it is described in the 2nd step. Put F end with coordinate on Ou's axis to it equal at = r/2 and a point of D with coordinate at =-r/2.
8. By means of the square build the line passing through the point of D perpendicular to an axis of symmetry of a parabola. This line – the head mistress of a parabola.
9. Take thread on length equal to one of square legs. Fix one end of thread by the button at top of the square to which this leg adjoins, and the second end – in parabola focus in F point. Put a ruler so that its upper edge coincided with the head mistress of D. On a ruler put the square, a leg, free from the button.
10. Establish a pencil so that it the edge pressed thread to a square leg. Move the square along a ruler. The pencil will draw a parabola necessary to you.