Essential Question:  How can we recognize situations that can best be modeled using quadratic and/or polynomial functions?  How can we find and use the zeros of a polynomial function to answer questions about a model?

Unit Rationale:  Review and explore quadratic functions-translate between standard, vert4ex, and factored forms of a quadratic equation; determine zeros of polynomial functions; learn techniques to determine the equation of a polynomial and to find roots of polynomials-in order to solve problems involving motion, minimum and maximum, and data that is best modeled with a quadratic function, and may lead to work with conic sections.

As a result of this unit, students will be able to:

Ø  Factor a quadratic equation

Ø  Complete the square

Ø  Translate between standard, factored, and vertex form of a quadratic equation

Ø  Use the quadratic formula

Ø  Find x-intercepts, vertex, y-intercept

Ø  Graph

Ø  Use finite differences to find the equation of a polynomial

Vocabulary:

·         Polynomial

·         Degree

·         Polynomial function

·         Monomial, binomial, trinomial

·         Model

·         Coefficient

·         Finite differences method

·         Quadratic function

·         General form, factored form, vertex form

·         Cubic function

·         Zeroes of a function

·         Factor theorem numbers

·         Imaginary numbers

·         Complex numbers

Focus Standards:

A2.1.C  solve problems that can be represented by quadratic functions and equations.

A2.2A  Explain how whole, integer, rational, real, and complex numbers are related, and identify the number system(s) within which a given algebraic equation can be solved.

A2.3.A  Translate between the standard form of a quadratic function, the vertex form, and the factored form;  graph and interpret the meaning of each form.

A2.3.B  Determine the number and nature of the roots of a quadratic function

A2.3.C  Solve quadratic equations and inequalities, including equations with complex roots.

A2.6.E  Determine if a bivariate data set can be better modeled with an exponential or a quadratic function and use the model to make predictions.

Support Standards:

A2.1.A  Select and justify functions and equations to model and solve problems.

Reasoning, Problem Solving, and Communication Standards:

A2.8.C  Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution in the context of the original problem.

A2.8.D  Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems.

A2.8.E  Read and interpret diagrams, graphs, and text containing the symbols, language and conventions of mathematics.

A2.8.F  Summarize mathematical ideas with precision and efficiency for a given audience and purpose.

A2.8.H   Synthesize information to draw conclusions and evaluate the arguments and conclusions of others.