# AII.6 - Quadratic Transformations

AII.6  For (quadratic) absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic functions, the student will

a)  recognize the general shape of function families; and

b)  use knowledge of transformations to convert between equations and the corresponding graphs of functions.

### BIG IDEAS

• I can find the correlation between different types of vehicles and the number of tires they have, the amount of money put into a vending machine and the kind of selection that comes out, and track the money I save over a year to determine when I can buy a cell phone.
• I will recognize that functions are mathematical representations of many input-output situations.

### UNDERSTANDING THE STANDARD

2016 VDOE Curriculum Framework - AII.6 Understanding

·  The transformation of a function, called a pre-image, changes the size, shape, and/or position of the function to a new function, called the image.

·  The graphs/equations for a family of functions can be determined using a transformational approach.

·  The graph of a parent function is an anchor graph from which other graphs are derived using transformations.

·  Transformations of functions may require the domain to be restricted.

·  Transformations of graphs include

­  Translations (horizontal and/or vertical shifting of a graph);

­  Reflections (over the x-axis and/or y-axis); and

­  Dilations (horizontal or vertical stretching and compressing of graphs).

· The reflection of a function over the line  represents the inverse of a function.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  AII.6a1  Recognize the general shape of function families.

·  AII.6b2  Write the equation of a function given the graph.

·  AII.6b1  Identify the graph of a function from the equation.

·  AII.6b3  Graph a transformation of a parent function, given the equation.

·  AII.6a2  Recognize graphs of parent functions.

·  AII.6b4  Identify the transformation(s) of a function. Transformations of exponential and logarithmic functions, given a graph, should be limited to a single transformation.

·  AII.61  Investigate and verify transformations of functions using a graphing utility.

### KEY VOCABULARY

absolute value, square root, cube root, rational, polynomial, exponential, logarithmic, transformational, symbolic form, graphic form, parent function, transformed function, pre-image

Updated: Aug 23, 2018