How can I write a rule that translates y=x^2 into y=(x+7)^2-4?"

Thanks for answering! It helped me a lot! 

I am not very familiar with this type of question but I think it is just

$$(x,y)\rightarrow (x-7,y-4)$$

I always find it easier if I write the second one like this    $$y+4=(x+7)^2$$

Look at the graphs.  That will help too.