Graph the function y = (x - 1)² + 3. How is the graph a translation of f(x) = x².

Solution:

The function y = (x - 1)² + 3 is a translation of the function f(x) = x².

If the function y = f(x) = x² is translated to the right by 1 unit because of the square of (x - 1)

y = f(x) = (x - 1)².

If the above function i.e. y = f(x) = (x - 1)² is translated up by 3 units we get

y = f(x) = (x - 1)² + 3

The graph of the translation is shown below:

Graph the function y = (x - 1)² + 3. How is the graph a translation of f(x) = x²

Summary:

The graph is a translation of f(x) = x² by moving 1 unit right and 3 units up.