The parabola is a schedule of square function, in a general view the equation of a parabola registers y=aх^2+bх + with where a0. It is a universal curve of the second order which describes many phenomena in life, for example, the movement thrown and then the falling body, a rainbow form therefore the ability find a parabola can be useful very much in life.
It is required to you
- - formula of the square equation;
- - sheet of paper with a coordinate grid;
- - pencil, eraser;
- - computer and Excel program.
1. First of all find parabola top. To find an abscissa of this point, take coefficient before x, divide it into the doubled coefficient before х^2 and increase by-1 (a formula x =-b/2a). Find ordinate, having substituted the received value in the equation or on a formula at = (b^2-4ac)/4a. You received parabola top point coordinates.
2. The top of a parabola can be found and in a different way. As the top is a function extremum, for its calculation calculate the first derivative and equate it to zero. In a general view you receive a formula f (x)' = (ax? + bx + c)' = 2ax + b. And having equated it to zero, you will come to the same formula - x =-b/2a.
3. Learn whether parabola branches up or down are directed. For this purpose look at coefficient before х^2, that is on and. If a> 0, branches are directed up if and
4. Construct an axis of symmetry of a parabola, it crosses top of a parabola and is parallel to an axis ou. All points of a parabola will be equidistanted from it therefore it is possible to construct only one part, and then symmetrically to display it concerning a parabola axis.
5. Build the line of a parabola. For this purpose find several points, substituting different values x in the equations and solving equality. It is convenient to find crossing with axes, for this purpose substitute in equality x =0 and at =0. Having constructed one party, reflect it symmetrically concerning an axis.
6. It is possible to construct a parabola by means of the Excel program. For this purpose open the new document and allocate in it two columns, x and at =f (x). In the first column write down values x on the chosen piece, and in the second column write down a formula, for example, = 2B3*B3-4B3+1 or =2В3^2-4В3+1. Not to write this formula every time, "stretch" it on all column, having pressed a mouse a small cross in the bottom right corner and having pulled down.
7. Having received the table, press the Insert menu - "Chart". Choose the dot chart, press "Further". In the appeared window add a row, having pressed the Add button. To choose the necessary cells, click serially on the buttons circled with a red oval below, then allocate your columns with values. Having pressed the button "Is ready", estimate result – a ready parabola.