Use completing the square:
Convert to
Where are the coordinates of the vertex.
The method I was thinking about is the following.
Given is the parabola: and the vertex point with coordinates
In general we know we can directly read the coordinates of the vertex of a parabola if we convert to:
where are the coordinates of the parabola.
First, divide every term by so:
Use completing the square in the RHS:
That means:
(1) (1)
(2) (2)
Substituting (1) in (2) gives:
Therefore the parabola with vertex is:
But as you see, the method sudharaka wants to use is easier.