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Transformations of Quadratic Functions

Transformations of Quadratic Functions 1.13 - Solution

arrow_back Return to Transformations of Quadratic Functions

We want to describe how to transform the parent function to the graph of the given quadratic function. To do so, we need to consider two possible transformations.

  1. Horizontal stretches and shrinks
  2. Reflections

Let's consider them one at the time.

Horizontal stretch or shrink

We have a horizontal stretch when is multiplied by a number greater than one. If is multiplied by a number whose absolute value is less than one, a horizontal shrink will take place.

In the given exercise, is multiplied by Therefore, the previous graph will be horizontally shrunk by a factor of


Whenever is multiplied by a negative number, we will have a reflection of the graph across the -axis.

Note how each -coordinate stays the same, and how each -coordinate changes its sign.

Final graph

Let's now graph the given function and the parent function on the same coordinate grid.

Finally, let's summarize all the transformations of the graph of

  • A horizontal shrink by a factor of
  • Reflection in the -axis