Determine all the transformations that have happened to f(x) = (x + 4)2 + 2 compared to f(x) = x2

Folow the steps to learn what transformations were determined.

Step-by-step explanation:

First we would have to graph the parent function which is f(x) = x^2. Start by finding your x and y values. Find the y values by plugging in the x values into the parent function.

X    Y

2    4

1     1

0    0

-1     1

-2    4

Once these points are plotted you can start determining what are the transformations. Find the difference between the parent function and f(x) = (x + 4)^2 + 2 by looking below.

Vertical Shifts:

f(x) + c moves up,

f(x) - c moves down.

Horizontal Shifts:

f(x + c) moves left,

f(x - c) moves right.

The parent function has to be transformed left 4 and up 2. In order to do this shift each point from earlier left 4 and then up 2. In conclusion you will have two functions graphed (parent function and the transformed function).