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

May 16, 2018

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 $f \left(x\right) = 3 {x}^{2} - 1$

This means that $f \left(x - 2\right) = 3 {\left(x - 2\right)}^{2} - 1$

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

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

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