Question

How to find vertex from a equation of parabola?

Answer 1

I am clearing my answer by using an ex.

let,
an equation

y2+4x-6y+13=0

y2-6y+9= -4x -4

(y-3)2 =-4(x+1)

to transfer the origin at the point(-1,3),we put

x+1 =X and y-3 = Y

the equation of given parabola takes from

Y2 = -4X

here,
4a = 4 ,a = 1

X = 0
x+1 = 0
x = -1

Y = 0
y-3 = 0
y=3

so vertex is(-2,3)