To translate any graph to the left 5 units, we replace `x` with `x+5,` giving `y=(x+5)^2.` Now, to shift this graph down 3 units, we subtract 3, getting
The way I thought about this when first learning was to shift the graph of `f(x)` to the left or right (in other words, horizontally), it makes sense that we should do something to the input, which is represented on the horizontal ` `axis. Thus, something like `f(x+5)` makes sense. To shift a graph up or down (vertically), we should do something to the output, which is just `f(x).` Thus, `f(x)-3` makes sense. Now if we combine the two we get
`g(x)=f(x+5)-3=(x+5)^2-3,` just as we got above. Here's the graph of `y=(x+5)^2-3` in red and `y=x^2` in black.