In order to shift the graph of a certain function vertically, you have to add a certain constant to its equation: the constant is positive if the shift is upwards, negative if the shift is downward.
In this case, we have to add -3 to the equation (i.e. subtract 3 from the equation), so we end up with
[tex]y=x^2 \mapsto y=x^2-3[/tex]
