# How do you sketch the graph of y=(x-4)^2 and describe the transformation?

May 19, 2017

see below

#### Explanation:

The graph of $y = {\left(x - 4\right)}^{2}$ is

graph{(x-4)^2 [-7.58, 12.42, -2.96, 7.04]}

The transformation from the parent graph $y = {x}^{2}$ can be seen as a shift 4 units to the right.

May 19, 2017

See explanation

#### Explanation:

The first step in any transformation problem is identify the parent function. We know the function is a parabola since the variable has a power of $2$

To begin graphing, we can start with graphing the parent function (that is $y = {x}^{2}$) first and work our way up from there:
graph{x^2 [-10, 10, -2, 5]}

If we recall our transformation rules, we would know that the graph $y = {\left(x - 4\right)}^{2}$ means that we shift the entire function $\textcolor{red}{4}$ units to the $\textcolor{red}{\text{right}}$ So our final function looks like this: graph{(x-4)^2 [-10, 10, -2, 5]}

Here is a graph with the original function and the final function just so you can see that all we really did was shift the function $4$ units to the right: graph{(y-x^2)(-y+x^2-8x+16)=0 [-8.764, 11.24, -0.88, 6.12]}

This table on transformation rules may be of good use: 