Definition: When a figure is moved to a new position without undergoing any rotation, then the new figure is said to have been translated to the new position.

The graph of a quadratic equation in the form y = (x - b)² + c is a translation of the parent graph y = x².

Here is an example.

Start with the graph of y = x² - shown as dotted in the diagram.

Slide the graph to the right 4 units.

This results in the equation changing to y = (x - 4)².

Then slide the graph up 3 units.

The equation has now become y = (x - 4)² + 3.