Question

How do you sketch the graph of `y=3(x-2)^2-1` and describe the transformation?

Answer 1

The transformation of the graph is: Shift to 2 units in the right direction (or towards positive x-direction).

Look explanation for graph.

Explanation:

let `f(x)=3x^2-1`

This means that `f(x-2)=3(x-2)^2-1`

Therefore, the graph of `f(x-2)` is a shift to 2 units in the POSITIVE x-direction, since it;s x-2.

Thus, the graph of `f(x-2)` would be the graph of `f(x)` shifted to two units in the right.

Thus the graph of `f(x-2)` would look like:
graph{3(x-2)^2-1 [-10, 10, -5, 5]}