vertex of parabola

In the previous post we have discussed about Permutation and Combination and In today's session we are going to discuss about vertex of parabola.


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In mathematics, parabolas are basically graphs which have equations of the form:

                                                F(x) = ax² + bx + c                             where a≠ 0,

In parabolas, there are both highest and lowest points depending upon where they are going to open up or down. These points are called vertex. Parabolas are basically used to justify many real life situations like height above ground of an object thrown upward, to check period of time after some time, to check the area of rectangle with a particular width, to check the maximum height of any object etc. In all these situations we need to find some co-ordinates which we get with the help of parabolas. In parabolas there is vertical line of symmetry which passes through its vertex. This line of symmetry helps us to find out co-ordinates. To understand the vertex of a parabola we take an example where we need to examine line of symmetry also. So we have an equation which is

                                                                F(x) = x² – 4x - 5

And we have to find out the vertex of parabola. Now to get the roots of 'x' we use the quadratic formula which is:

                                                                X = [-b ±√(b² – 4ac)]/ 2a,

Where the values of a, b and c are 1, -4 and 5 in the equation. Now we put these values in above equation. So

                                                                X= - ( - 4)±√((-4)² – 4(1) (-5) ) / 2(1),

After solving further we get         x = (4 ± 6) / 2 = 2 ± 3,

These value is also called as x- intercept. Above point shows that it starts from 2 and add 3 to get one intercept, and when we subtract 3 from 2 we get another intercept. So 2 is the midpoint of two intercepts. Finally, we have intercept points which is 5 and -1. Now if we find 'y' value which passes through 'x' value then we put 'x' value in the given equation so

                                                                F(2) = (2)² – 4(2) – 5 = -9,

So the vertex of parabola is (2, -9).

Next we will discuss How to Calculate Molar Mass.

Cbse sample papers 2013 are available online.