Question

How do you identify transformations in parent functions given `y = 2(x-3)^2`?

Answer 1

Look at the `a`-value and `h`-value (and the `k`-value): the `a`-value transforms the parabola. The `h` and `k`-value translates the parabola.

In this case, the transformed parabola has a vertical stretch by a factor of `2` and is translated `3` units to the right.

Explanation:

The parent function if `y=x^2`, which looks like this:
graph{x^2 [-10, 10, -5, 5]}

The transformed function, `y=2(x-3)^2` is a lot more simpler to determine it's transformation because it is given in vertex form.

There are two main things being done to the parabola.

1. The `a`-value - having a value greater than `1` as the `a`-value indicates a vertical stretch by a factor of whatever was used. In this case, `2`.
2. The `h`-value translates the parabola to the left or right. It is determined by isolating the `x`-value in the bracket (AND BRACKET ONLY). In this case, the parabola is moved `3` units to the right.

It looks like this:

graph{2(x-3)^2 [-10, 10, -5, 5]}

Hope this helps :)