# How do you graph y=(x-3)^2+1?

May 6, 2017

See explanation

#### Explanation:

Know that the parent function is $y = {x}^{2}$. This is where we start and so our starting function looks like this:

$y = {x}^{2}$ graph{x^2 [-10.04, 9.96, -1, 9]}

Looking at just $y = {\left(x - 3\right)}^{2}$ the fact that the $- 3$ is on the $\textcolor{red}{\text{inside}}$ of the $\left(\right)$ it tells us that the function is shifted or translated $3$ units to the $\textcolor{red}{\text{right}}$.

Thus far, our function looks like this:

$y = {\left(x - 3\right)}^{2}$ graph{(x-3)^2 [-5.45, 14.55, -1, 9]}

Lastly, looking at the entire function $y = {\left(x - 3\right)}^{2} + 1$, the $1$ tells us to shift or translate the function $1$ unit $\textcolor{red}{\text{upward}}$.

Our final function will then look like this:

$y = {\left(x - 3\right)}^{2} + 1$ graph{(x-3)^2+1 [-5.41, 14.59, -0.64, 9.36]}

In essence the questions asks you to apply certain transformation rules. I provided a chart of the transformations you should be aware of.