Question

What required transformations are needed to convert the graph of `y=2(x+3)^4+(x+3)^2+x+7` to the graph of `y=2x^4+x^2+x`?

Answer 1

The coordinate translation

`{(x = X-3),(y = Y + 4):}`

Explanation:

Making `X = x+3` and `Y = y - 4` we have

`Y+4=2X^4+X^2+X-3+7`

so, after the translation we have

`Y = 2X^4+X^2+X`