Question

How do you sketch the graph of `y=(x-8)^2` and describe the transformation?

Answer 1

Draw `8` units to the right. That is the only transformation done.

Explanation:

The easiest way we can do is to graph it and describe what changes were made from the parent function, `y=x^2`.

This is a little easier because the equation given is in vertex form.

There is only thing changed:

The `h`-value. The `h`-value provides the horizontal translations, where we have to isolate the value from `x` within the bracket.

Thus, `-8 -> 8` (because we bring it over to equal to `x`).

Everything else stayed the same: `a`-value, `k`-value.

Because everything stayed the same, in terms of drawing, just draw the parabola, `8` units to the right, instead of at the origin.

Transformed function:

graph{(x-8)^2 [-10, 10, -5, 5]}

Parent function:

graph{x^2 [-10, 10, -5, 5]}

Hope this helps :)