# Standard 6: Solve and graph polynomial equations and functions in one and two variables.

General Information
Number: MA.912.AR.6
Title: Solve and graph polynomial equations and functions in one and two variables.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.912.AR.6.AP.1
Solve one-variable polynomial equations of degree 3 or higher in factored form, over the real number system.
MA.912.AR.6.AP.5
Create a rough graph of a polynomial function of degree 3 or higher (in factored form) using zeros, multiplicity and knowledge of end behavior.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

## Formative Assessments

Zeros of a Cubic:

Students are asked to identify the zeros of cubic polynomials, without the use of technology, and then describe what the zeros indicate about the graph.

Type: Formative Assessment

Use Zeros to Graph:

Students are given the factored form of a cubic polynomial and are asked to use the zeros to sketch the graph between two given points on the coordinate plane without the use of technology.

Type: Formative Assessment

## Lesson Plans

Taming the Behavior of Polynomials:

This lesson will cover sketching the graphs of polynomials while in factored form without the use of a calculator.

Type: Lesson Plan

This lesson introduces students to the Fundamental Theorem of Algebra. Polynomials that are not in factored form will be limited to quadratic and cubic polynomials.

Type: Lesson Plan

Where did the answers go? Oh, they're imaginary!:

In this lesson, students will solve quadratic equations with imaginary (complex) solutions and be facilitated in the discovery of the Fundamental Theorem of Algebra.

Type: Lesson Plan

Dancing Polynomials/Graph Me Baby:

Dancing Polynomials is designed to lead students from the understanding that the equation of a line produces a linear pattern to the realization that using an exponent greater than one will produce curvature in a graph and that further patterns emerge allowing students to predict what happens at the end of the graph. Using graphing calculators, students will examine the patterns that emerge to predict the end behavior of polynomial functions. They will experiment by manipulating equations superimposed onto landmarks in the shape of parabolas and polynomial functions. An end behavior song and dance, called "Graph Me Baby" will allow students to become graphs to physically understand the end behavior of the graph.

Type: Lesson Plan

## Perspectives Video: Expert

Problem Solving with Project Constraints:

<p>It's important to stay inside the lines of your project constraints to finish in time and under budget. This NASA systems engineer explains how constraints can actually promote creativity and help him solve problems!</p>

Type: Perspectives Video: Expert

## Perspectives Video: Teaching Idea

Multiplying Polynomials:

Unlock an effective teaching strategy for teaching multiplying polynomials in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

## Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

## Perspectives Video: Expert

Problem Solving with Project Constraints:

<p>It's important to stay inside the lines of your project constraints to finish in time and under budget. This NASA systems engineer explains how constraints can actually promote creativity and help him solve problems!</p>

Type: Perspectives Video: Expert

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

## Perspectives Video: Expert

Problem Solving with Project Constraints:

<p>It's important to stay inside the lines of your project constraints to finish in time and under budget. This NASA systems engineer explains how constraints can actually promote creativity and help him solve problems!</p>

Type: Perspectives Video: Expert