Question

What effect will replacing `x` with `(x-7)` have on the graph of the equation `y=(x+4)^2`?

Answer 1

The graph will shift 7 places to the right

Explanation:

For the graph of an equation `y=(x+4)^2` a zero will occur at the point `x=-4` `(-4+4)^2=0^2=0`

If we use `(x-7)` instead of `x` we get `y=(x-7+4)^2-=(x-3)^2`. A zero will now occur at `x=3`, as `(3-3)^2=0^2=0`.

What you may notice is that by taking away `7` to `x`, the zeros of the graph shift by `7` to the right.

`y=(x+4)^2`, zero occurs at `-4`
`y=(x-7+4)^2-=(x-3)^2`, zero occurs at `3`

`3-(-4)=3+4=7`

`(x+4)-(x-3)=x+4-x+3=0+4+3=7`