If has an analytic job functions, and bring it to standard form: A*x2+B*x+C=y(x), where A is a senior the coefficient of x2, B is the average coefficient of x, C − free member. Note that the coecient of x2 is not equal to zero, otherwise it will not be a quadratic function.
Coordinate of the vertex x0 on the x-axis is given by: x0=-B/2A. In the case of a given quadratic equation, that is, when A=1, the formula simplifies to: x0=-B/2. If the equation has no "xa" in the first degree, then the coefficient B=0, then x0 also goes to zero.
To find the coordinate of the vertex of the parabola on the y-axis, substitute the value obtained for x0 in the equation. When you simplify the expression on the one hand you have "y" on the other − a number of Q. It shows the ordinate of the vertex: y0=Q.
Thus, the study analytically given function gave you a point on the graph with coordinates (x0;y0). If the lead coefficient A > 0, the branches of the parabola are directed upwards, and the top period of decrease will be replaced by a period of growth. If A < 0, the branches of the parabola are directed downwards, and in this case the increase of the function at the top will change to the descending.
Since x0 is a point of extremum of the function, its numerical value can be found by differentiation. Find the first derivative of the function. Paranaita it to zero and solve the resulting equation. He will satisfy only the value of x, which is the coordinate of the vertex of the parabola.
If you need to mention "x is zero" on the chart, swipe from the vertex of a parabola a dotted line perpendicular to the x-axis. The point where the perpendicular crosses the x-axis, a label for x0. To see the chart for "y is zero", swipe from the top perpendicular respectively to the y-axis.