Question

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

Answer 1

There are two transformations applied to the graph: a vertical stretch by a scale factor of 2 and a translation 2 units to the right.

Explanation:

In order to sketch the graph, know that the vertex will be `(2,0)`. After this, plug values into the equation and plot them. Here are some points that should help you:

`(0,8)`
`(1,2)`
`(2,0)`
`(3,2)`
`(4,8)`

Here's the graph:

graph{2(x-2)^2 [-8, 12, -1, 9]}