Question

How is the graph of y=(x-1)^2-3 transformed to produce the graph of y=1/2(x+4)^2

Answer 1

To transform the graph of y = (x-1)^2 - 3 to produce the graph of y = 1/2(x+4)^2, we can use the following steps:

1. Shift the graph of y = (x-1)^2 to the right by 4 units. This can be done by adding 4 to the x-values of every point on the graph.
2. Stretch the graph vertically by a factor of 2. This can be done by multiplying the y-values of every point on the graph by 2.
3. Shift the graph upward by 3 units. This can be done by adding 3 to the y-values of every point on the graph.

Applying these transformations to the graph of y = (x-1)^2 will produce the graph of y = 1/2(x+4)^2.