Question

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

Answer 1

see below

Explanation:

The graph of `y = (x-4)^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.

Answer 2

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=(x-4)^2` means that we shift the entire function `color(red) 4` units to the `color(red)("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: