Answer: g(x) = (x - 2)^2 + 3
Step-by-step explanation:
First, let's define the two transformations:
Vertical shift.
If we have a function f(x), a vertical shift of N units is written as:
g(x) = f(x) + N
This will move the graph of f(x) up or down a distance of N units.
if N is positive, then the shift is upwards
if N is negative, then the shift is downwards.
Horizontal shift.
If we have a function f(x), a horizontal shift of N units is written as:
g(x) = f(x + N)
This will move the graph of f(x) to the right or left a distance of N units.
if N is positive, then the shift is to the left
if N is negative, then the shift is to the right.
Then we start with the function f(x) = x^2
A shift of 3 units up is written as:
g(x) = f(x) + 3
And a shift of 2 units to the right is written as:
g(x) = f(x - 2) + 3
Replacing by the original function we get:
g(x) = (x - 2)^2 + 3
