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### Chapter 9--Quadratic Models

 Essential Question:  How can we use graphs, words, tables, and different forms of equations to model quadratic relationships and solve problems? Unit Rationale:  Quadratic functions model many real-life situation, such as trajectories, shapes of objects, and maximum/minimum values. As a result of this unit, students will be able to: Ø  Write, solve, and graph problems using vertex, factored, and general form of the quadratic function. Ø  Change a quadratic function from one form (factored) to another (general) and justify when and when such a change should be made. Ø  Use multiple representations to model quadratic functions Ø  Use the quadratic formula, factoring, and completing the square to solve equations. Vocabulary: ·        Binomial ·        Completing the square ·        Discriminant ·        Factored form ·        General form ·        Gravity ·        Line of symmetry ·        Monomial ·        Perfect square ·        Polynomial ·        Quadratic formula ·        Quadratic function ·        Radical expression ·        Real number ·        Roots ·        Term ·        Vertex form ·        X-intercepts ·        Zero-product property ·        Zeros Standards: Standards will be assessed on both the state and classroom levels, however, standards with an asterisk (*) in the code will count for graduation requirements.  Focus Standards: A1.1.D  Solve problems that can be represented by quadratic functions and equations. A1.5.A  Represent a quadratic function with a symbolic expression, as a graph, in a table, and with a description, and make connections among the representations. Supporting Standards: A1.5.B  Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the x-intercepts as solutions to a quadratic equation. A1.5.C Solve quadratic equations that can be factored as (ax+b)(cx+d) where a, b, c, and d are integers. A1.5.D   Solve quadratic equations that have real roots by completing the square and by using the quadratic formula. *A1.2.B  Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables. A1.2.E  Use algebraic properties to factor and combine like terms in polynomials. Reasoning, Problem Solving, and Communication Standards: A1.8.A  Analyze a problem situation and represent it mathematically. A1.8.B  Select and apply strategies to solve problems.