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# Standard #: MAFS.912.F-IF.3.8 (Archived Standard)

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Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
1. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
2. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = , y = , y = , y = , and classify them as representing exponential growth or decay.

### General Information

Subject Area: Mathematics
Domain-Subdomain: Functions: Interpreting Functions
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Analyze functions using different representations. (Algebra 1 - Supporting Cluster) (Algebra 2 - Supporting Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

### Test Item Specifications

Also assesses:

MAFS.912.A-APR.2.3

MAFS.912.F-IF.3.7

Assessment Limits :
For F-IF.3.7, items are limited to linear, quadratic, and exponential
functions.

For A-APR.2.3, the leading coefficient should be an integer and the
polynomial’s degree is restricted to 3 or 4. The polynomial function
should not have a zero with multiplicity. The polynomial should be
given in factored form.

For F-IF.3.8a, items that require the student to transform a quadratic
equation to vertex form, b/a must be an even integer.

For F-IF.3.7e and F-IF.3.8b, exponential functions are limited to simple
exponential growth and decay functions and to exponential functions
with one translation. Base e should not be used.

For F-IF.3.8, items may specify a required form using an equation or using common terminology such as standard form. In items that require the student to interpret the vertex or a zero of a quadratic function within a real-world context, the student should interpret both the x-value and the y-value.

For F-IF.3.7a, quadratic functions that are given in the form y = ax² + bx + c, a, b, and c must be integers. Quadratic functions given in vertex form y = a(x – h)² + k, a, h, and k must be integers. Quadratic functions given in other forms should be able to be rewritten and adhere to one of the two previous forms.

Calculator :

Neutral

Clarification :
Students will identify zeros, extreme values, and symmetry of a

Students will classify the exponential function as exponential growth
or decay by examining the base, and students will give the rate of
growth or decay.

Students will use the properties of exponents to interpret exponential
expressions in a real-world context.

Students will write an exponential function defined by an expression
in different but equivalent forms to reveal and explain different
properties of the function, and students will determine which form of
the function is the most appropriate for interpretation for a realworld context.

Students will find the zeros of a polynomial function when the
polynomial is in factored form.

Students will create a rough graph of a polynomial function in
factored form by examining the zeros of the function.

Students will use the x-intercepts of a polynomial function and end
behavior to graph the function.

Students will identify the x- and y-intercepts and the slope of the
graph of a linear function.

Students will identify zeros, extreme values, and symmetry of the

Students will identify intercepts and end behavior for an exponential
function.

Students will graph a linear function using key features.

Students will graph a quadratic function using key features.

Students will graph an exponential function using key features.

Students will identify and interpret key features of a graph within the
real-world context that the function represents.

Stimulus Attributes :
Items may require the student to identify a correct graph.

Items may be set in a mathematical or real-world context.

For F-IF.3.8, items must use function notation.

For F-IF.3.7, items may use an equation or a function.

Items should not require the student to complete a sign chart for a
polynomial.

Response Attributes :
For F-IF.3.7, items may require the student to apply the basic
modeling cycle.

Items may require the student to choose an appropriate level of
accuracy.

Items may require the student to choose and interpret the scale in a
graph.

Items may require the student to choose and interpret units.

Items may require the student to provide the answer in a specific
form.

Responses with square roots should require the student to rewrite
the square root so that the radicand has no square factors.

### Sample Test Items (2)

 Test Item # Question Difficulty Type Sample Item 1 A bird drops a stick from the top of Miami Tower. The height of the stick after x seconds is given by f(x)=625-16x²Select all the correct interpretations of the coordinates of the point at the maximum of the function f(x). N/A MS: Multiselect Sample Item 2 A bird drops a stick from the top of Miami Tower. The height of the stick after x seconds is given by f(x)= 625-16x².What is the maximum value of f(x)? N/A EE: Equation Editor

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#### Formative Assessments

 Name Description Exponential Functions - 2 Students are asked to identify the percent rate of change of a given exponential function. Exponential Functions - 1 Students are asked to identify the percent rate of change of a given exponential function. A Home for Fido Students are asked to rewrite a quadratic function in an equivalent form by completing the square and to use this form to identify the vertex of the graph and explain its meaning in context. Launch From a Hill Students are asked to factor and find the zeros of a polynomial function given in context.

#### Perspectives Video: Expert

 Name Description Using Mathematics to Optimize Wing Design Nick Moore discusses his research behind optimizing wing design using inspiration from animals and how they swim and fly. Download the CPALMS Perspectives video student note taking guide.

 Name Description Which Function? The task addresses knowledge related to interpreting forms of functions derived by factoring or completing the square. It requires students to pay special attention to the information provided by the way the equation is represented as well as the sign of the leading coefficient, which is not written out explicitly, and then to connect this information to the important features of the graph. Springboard Dive The problem presents a context where a quadratic function arises. Careful analysis, including graphing of the function, is closely related to the context. The student will gain valuable experience applying the quadratic formula and the exercise also gives a possible implementation of completing the square.

#### Tutorial

 Name Description Power of a Power Property This tutorial demonstrates how to use the power of a power property with both numerals and variables.

#### Unit/Lesson Sequence

Name Description
Sample Algebra 1 Curriculum Plan Using CMAP

This sample Algebra 1 CMAP is a fully customizable resource and curriculum-planning tool that provides a framework for the Algebra 1 Course. The units and standards are customizable and the CMAP allows instructors to add lessons, worksheets, and other resources as needed. This CMAP also includes rows that automatically filter and display Math Formative Assessments System tasks, E-Learning Original Student Tutorials and Perspectives Videos that are aligned to the standards, available on CPALMS.

Learn more about the sample Algebra 1 CMAP, its features and customizability by watching the following video:

### Using this CMAP

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All CMAP tutorials can be found within the iCPALMS Planner App or at the following URL: http://www.cpalms.org/support/tutorials_and_informational_videos.aspx

#### Video/Audio/Animations

 Name Description Solving Quadratic Equations using Square Roots This video will demonstrate how to solve a quadratic equation using square roots. Quadratic Functions 2 This video gives a more in-depth look at graphing quadratic functions than previously offered in Quadratic Functions 1.

#### Worksheet

 Name Description Quadratic Functions This worksheet gives students one place to show all transformations (reflections, vertical stretches/compressions, and translations) for the quadratic function. The worksheet also has a place for domain and range for each transformation.

#### Student Resources

 Name Description Which Function?: The task addresses knowledge related to interpreting forms of functions derived by factoring or completing the square. It requires students to pay special attention to the information provided by the way the equation is represented as well as the sign of the leading coefficient, which is not written out explicitly, and then to connect this information to the important features of the graph. Springboard Dive: The problem presents a context where a quadratic function arises. Careful analysis, including graphing of the function, is closely related to the context. The student will gain valuable experience applying the quadratic formula and the exercise also gives a possible implementation of completing the square.

#### Tutorial

 Name Description Power of a Power Property: This tutorial demonstrates how to use the power of a power property with both numerals and variables.

#### Video/Audio/Animations

 Name Description Solving Quadratic Equations using Square Roots: This video will demonstrate how to solve a quadratic equation using square roots. Quadratic Functions 2: This video gives a more in-depth look at graphing quadratic functions than previously offered in Quadratic Functions 1.