How do you find the vertex of a parabola with any given equation?

a detailed explanation is much appreciation: )

There are lots of ways to find the vertex. It depends on the way the equation of the parabola is found. 

if it is in the form 

     where a, b, c are constants

1. The vertex is on the line of symmetry of the parabola. this can be found by using 



then substitute this value into the equation to find the corresponding y value. 

e.g. if you have a  parabola



a = -6, b = 1 and c = 4

the line of symmetry is 



the line of symmetry is x = 3   now substitute 



y = 13 is the maximum for the curve.

so the vertex is at (3, 13)

hope it makes sense. 

There are other methods that involve completing the square 

I just find this easy