Florida B.E.S.T. MA.912.AR.6

MA.912.AR.6 is a B.E.S.T. standard. These are the benchmarks under it.

• MA.912.AR.6.1

  Given a mathematical or real-world context, when suitable factorization is possible, solve one-variable polynomial equations of degree 3 or higher over the real...

• MA.912.AR.6.2

  Explain and apply the Remainder Theorem to solve mathematical and real-world problems.

• MA.912.AR.6.3

  Explain and apply theorems for polynomials to solve mathematical and real-world problems.

• MA.912.AR.6.4

  Given a table, equation or written description of a polynomial function of degree 3 or higher, graph that function and determine its key features.

• MA.912.AR.6.5

  Sketch a rough graph of a polynomial function of degree 3 or higher using zeros, multiplicity and knowledge of end behavior.

• MA.912.AR.6.6

  Solve and graph mathematical and real-world problems that are modeled with polynomial functions of degree 3 or higher. Interpret key features and determine cons...

01

What Students Need to Do

Students solve polynomial equations by factoring, graphing, or using appropriate technology, then check their solutions. They graph polynomial relationships and connect roots, intercepts, multiplicity, degree, and end behavior.

02

What Mastery Looks Like

Students find and check real roots, including repeated roots. They produce a graph with correct intercepts, turning behavior, and end behavior, and recognize that each point represents a solution pair.

03

Common Misconceptions

Students may divide by a variable factor and lose the zero solution. They may confuse roots with y-intercepts, or assume every root crosses the x-axis instead of sometimes touching it.

04

How to Assess It

Give students f(x) = (x + 1)(x - 2)². Ask them to list the roots, state where the graph crosses or touches, and sketch its end behavior.

1. 01

   Have students arrange root, multiplicity, and end-behavior cards, then draw the matching polynomial graph on chart paper.

2. 02

   Ask students to explain how two polynomials can have the same roots but different graphs because of multiplicity or leading coefficient.

3. 03

   Run a card match with polynomial equations, factored forms, root lists, and graphs placed at four stations.

4. 04

   Model an open box with a cubic volume function, then graph it and solve for dimensions that produce a target volume.

• MA.912.AR.3

  Write, solve and graph quadratic equations, functions and inequalities in one and two variables.

• MA.912.AR.5

  Write, solve and graph exponential and logarithmic equations and functions in one and two variables.

• MA.912.AR.8

  Solve and graph rational equations and functions in one and two variables.

• MA.912.AR.7

  Solve and graph radical equations and functions in one and two variables.