Write function in vertex form

can you show me how to turn this equation into vertex form? Step by step please

y=x^2-4x+7

And how to turn this equation into intercept form:
y=x^2+2x-3


Please and thank you :)

y = x^2 - 4x + 7
y = x^2 - 4x + (4/2)^2 + 7 - (4/2)^2
y = (x + (4/2))^2 + 7 - 4
y = (x + 2)^2 + 3

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