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

1 Answer
Apr 22, 2017

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 :)