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If we subtract a number off...

y = x^2 - 3
This takes 3 off of each of the outputs (the y guys).

So...

y = x^2

y = x^2 - 3

graph of y = x^2

graph of y = x^2 - 3

 

Moves Standard Parabola Guy down 3

 

Check out this animation to see how I work through these things: