# Y= x^2 is translated 3 units to the right and 1 unit up?

Mar 1, 2017

$y = {\left(x - 3\right)}^{2} + 1$

#### Explanation:

In general if a function is translated $a$ units right and $b$ units up we can summaries this as:

$f \left(x\right) \text{ translated by } \left(\begin{matrix}a \\ b\end{matrix}\right) \rightarrow f \left(x - a\right) + b$

so $\text{ "Y=x^2" translated by 3 units right, " 1 " unit up}$

$Y = {x}^{2} \text{ translated by } \left(\begin{matrix}3 \\ 1\end{matrix}\right) \rightarrow y = {\left(x - 3\right)}^{2} + 1$