Transformations of Quadratic Functions

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Questions and Answers

What effect does replacing f(x) with f(x) + k have on the graph of a quadratic function?

It shifts the graph up or down. (correct)
It stretches the graph vertically.
It rotates the graph around the origin.
It reflects the graph over the x-axis.

When analyzing the transformation of the function f(x) to kf(x), what does a positive value of k indicate?

The graph is compressed vertically.
The graph remains unchanged.
The graph is stretched vertically. (correct)
The graph is reflected over the y-axis.

If a quadratic function is transformed using f(kx), what aspect of the graph is affected by a value of k greater than 1?

The graph shifts vertically.
The graph shifts to the right.
The graph reflects over the x-axis.
The graph compresses horizontally. (correct)

What does the transformation f(x + k) accomplish when k is negative?

<p>It shifts the graph to the left. (B)</p> Signup and view all the answers

How can you determine the value of k from the graphs of two quadratic functions?

<p>By comparing their vertex positions. (C)</p> Signup and view all the answers

Flashcards

Vertical translation (f(x) + k)

A transformation of a quadratic function where the graph is shifted up or down by a constant value 'k'.

Vertical Stretch/Compression (kf(x))

A transformation of a quadratic function where the graph is stretched or compressed vertically by a factor of 'k'.

Horizontal Stretch/Compression (f(kx))

A transformation of a quadratic function where the graph is stretched or compressed horizontally by a factor of '1/k'.

Horizontal Translation (f(x + k))

A transformation of a quadratic function where the graph is shifted left or right by a constant value of '-k'.

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Vertex of a Quadratic Function

The point on the graph of a quadratic function where the curve changes direction. It is also the point where the quadratic function reaches its maximum or minimum value.

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Study Notes

Transformations of Quadratic Functions

Students will learn how changing parts of a quadratic function's equation (like adding a constant, multiplying by a constant, or changing the input) affects the graph.
Identifying the transformation type from comparing graphs.
Determining the constant 'k' value from a graph.
Graphing the transformed quadratic function given the equation.
Writing equations for transformed quadratic functions based on descriptions and the original (parent) quadratic function.
Understanding positive and negative values of 'k' in relation to the graph transformations as well.

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Description

This quiz focuses on the transformations of quadratic functions, exploring how changes in the equation affect the graph. Students will identify transformation types, graph transformed functions, and write equations based on descriptions. A key component includes understanding the role of constant 'k' in these transformations.