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Unit 6

Quadratics

Unit Description

    In this unit, students will explore polynomials by finding the degree, state the type given the number of terms and degree, and add, subtract and multiply polynomials (limit to addition and subtraction of quadratics and multiplication of linear expressions). Students will factor a quadratic expression to reveal the zeros of the function it defines. They will look at the graphs of quadratic functions and identify key characteristics of the graph. The students will then use quadratic functions to model real-life contexts (such as projectile motion and maximizing area) and use the model to solve problems. Quadratic functions will be compared to linear and exponential functions in terms of key characteristics and growth.


Unit Skills 
  • I can determine whether an expression is a polynomial (A-APR.1).
  • I can add, subtract, multiply polynomials (limit to addition and subtraction of quadratics and multiplication of linear expressions) (A-APR.1).
  • I can identify the coefficients and constants of a quadratic function and interpret them in a contextual situation (A-SSE.1a).
  • I can sketch the graph of a quadratic function and interpret key features in context, including domain, range, intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximum or minimum; and symmetry (F-IF.4; A-CED.2).
  • I can determine if a function is a quadratic function (F-BF.1).
  • I can use quadratic functions to model relationships between two quantities (F-BF.1).
  • I can factor a quadratic expression to reveal the zeros of the graph of the function (A-SSE.2; A-SSE.3).
  • Given a quadratic function in context, I can determine the practical domain of the function (input values that make sense to the constraints of the problem context) (F-IF.4).
  • I can determine the appropriate viewing window and scale to reveal the key features of the graph of a quadratic function (N-Q.1).
  • I can recognize equivalent forms of quadratic functions. For example, standard form y = ax2+bx+c, and factored form y = a(x - r1)(x - r2) (A-SSE.2).
  • I can compare properties of two quadratics each represented in a different way (algebraically, graphically, numerically in tables, or by verbal description) (F-IF.9).
  • Given different forms of various linear, exponential, and quadratic functions, I can determine which forms represent linear, exponential, and quadratic functions (F-IF.9).
  • Using graphs or tables, I can show that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically (F-LE.3).


Unit 6 Plan




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