Write a function that represent the parent function y=x^2 after it has been translated 3 up and 2 right

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

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step-by-step explanation:

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