Why do some quadratic graphs move left or right and others do not? Is there a correlation between this and them moving up and down? How would you demonstrate your reasoning is correct?

(x + 3) ^2 is left 3 because it becames 0 at - 3

(x - 3) ^2 is right 3 because it becames 0 at 3

x^2 + 3 is up 3 because your just adding 3 units up

x^2 - 3 is down 3 because your just subtracting 3 units down