can i have some help with quadratic equations

[CmptrGk]

i have an algebra test tomorrow and i really don't understand how to convert standard form (y=ax^2+bx+c) to vertex (y=a(x-h)^2+k). and vice versa

this is what i have for notes on the subject but i don't get it

vertex -> standard
y=2(x+1)^2-3
2(x+1)(x+1)
2[x^2+2x+1]-3
2x^2+4x+2-3
2x^2+4x-1
y=2x^2+4x-1

i really have no clue how this process works, i would like it if some1 could explain it to me


also standard -> vertex
f(x)=2x^2-4x+1
1.)Find vertex
(-b/2a, f(-b/2a)) vertex formula???

a=2 (-b/2a f(1)=2(1)^2-4(1)+1
b=-4 (-(-4)/2(2) = 2-4 +1
c=1 (4/4 = -2-1
=-1

vertex (1,-1)
h k

y=2(x-1)^2-1


i also have no clue how this works also