# 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?

Aug 31, 2016

The coordinate translation

$\left\{\begin{matrix}x = X - 3 \\ y = Y + 4\end{matrix}\right.$

#### Explanation:

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

$Y + 4 = 2 {X}^{4} + {X}^{2} + X - 3 + 7$

so, after the translation we have

$Y = 2 {X}^{4} + {X}^{2} + X$