Question

Graph $f\left(x\right)=2{(x+1)}^2-4$using transformations.

Short answer

The graph is:

Step-by-step solution

Step 1. Given information

The given function is:$y=2{(x+1)}^2-4$

Step 2. The graph of y=x2:

Step 3. The graph of y=(x+1)2

Shift horizontally above graph by 1 unit towards left.

Step 4. Graph of y=2(x+1)2

Increase the width of the above graph by a factor of 2.

Step 5. The graph of y=2(x+1)2-4

Vertically shift the above graph by 4 units to the down.