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Describing Transformations of Quadratic Functions

Describing Transformations of Quadratic Functions 1.9 - Solution

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To determine the quadratic function that is obtained from the parent function after the given sequence of transformations, let's consider the transformations one at a time.

Horizontal Stretch by a Factor of

We'll start by performing a horizontal stretch of the parent function by a factor of This is done by multiplying the -variable by The resulting function is

Vertical Translation Units Up

Next, to perform a vertical translation units up we need to add to the whole function. The result is

Reflection in the -axis

Finally, let's reflect the function across the -axis by multiplying the variable by This will not affect the graph since

The quadratic function that is obtained after the sequence of transformations is

Vertex

The vertex of let's rewrite it into vertex form. This is done by subtracting from Therefore, the vertex of is