Instruction

1

To find the coordinates of the vertex

**of the parabola**, use the following formula: x=-b/2A, where a is the coefficient in front of x squared, and b is the coefficient in front of X. Substitute your values and calculate its value. Then substitute the resulting value is x in the equation and calculate the y coordinate of the vertex. For example, if you are given the equation y=2x^2-4x+5, then find the abscissa in the following way: x=-(-4)/2*2=1. Substituting x=1 into the equation, calculate the value of y for the vertex**of a parabola**: =2*1^2-4*1+5=3. Thus, the vertex**of the parabola**has coordinates (1;3).2

The value of the ordinates

**of the parabola**can be found without preliminary calculation of the abscissa. Use the formula y=-b^2/4 ° C+S.3

If you are familiar with the concept of the derivative, find

**the vertex****of a parabola**using derivatives, using the following property of any functions: the first derivative equal to zero indicates extreme points. Since the vertex**of the parabola**, regardless of the sent its branches upwards or downwards, is a point of extremum, calculate derivative for your function. In General it will be of the form f(x)=2ах+b. Paranaita it to zero and get the coordinates of the vertex**of the parabola**corresponding to your function.4

Try to find

**the vertex****of a parabola**using such property as symmetry. To do this, find the point of intersection**of the parabola**with the axis ox, equating the function to zero (substituting y=0). Solving the quadratic equation, you will find x1 and x2. Since the parabola is symmetric with respect to the directrix passing through**the vertex**, those points will be equidistant from the abscissa of the vertex. To find it, divide the distance between points in half: x=(Іх1-х2І)/2.5

If any of the coefficients is zero (except a), calculate the coordinates of the vertex

**of a parabola**on a lightweight formula. For example, if b=0, the equation has the form y=Ah^2+C, the vertex will lie on the axis Oy and its coordinates will be zero (0;off). If not only the coefficient b=0 but C=0, the vertex**of the parabola**is at the origin, the point (0;0).