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What is the relationship between the graph of a polynomial function and its equation or solutions?
ESSENTIAL QUESTION:

I will be able to:
  • identify key features of polynomial graphs & their transformations (5.1, 5.10, 5.11)
  • perform operations on polynomial expressions (5.2, 5.3, 5.4)
  • factor polynomials using various methods & use factoring to solve & write polynomial equations (5.5, 5.6, 5.7, 5.8, 5.9)

5: polynomial functions

5.1: Graphs of Polynomial Functions5.10: Transformations of Polynomial Functions5.11: Characteristics of Polynomial FunctionsA2.F.1.2 - Identify the parent forms of exponential, radical (square root and cube root only), quadratic, and logarithmic functions. Predict the effects of transformations [𝑓(π‘₯ + 𝑐), 𝑓(π‘₯) + 𝑐, 𝑓(𝑐π‘₯), π‘Žπ‘›π‘‘ 𝑐𝑓(π‘₯)] algebraically and graphically. A2.F.1.5 - Analyze the graph of a polynomial function by identifying the domain, range, intercepts, zeros, relative maxima, relative minima, and intervals of increase and decrease.

5.5: Factor Polynomials by GCF5.6: Factor Sum & Difference of Cubes5.7: Factor by Grouping5.8: Solve by Factoring or Graphing5.9: Write Polynomial EquationsA2.A.2.1 - Factor polynomial expressions including, but not limited to, trinomials, differences of squares, sum and difference of cubes, and factoring by grouping, using a variety of tools and strategies.A2.A.1.4 - Solve polynomial equations with real roots using various methods (e.g., polynomial division, synthetic division, using graphing calculators or other appropriate technology).

5.2: Add & Subtract Polynomials5.3: Multiply Polynomials5.4: Divide PolynomialsA2.A.2.2 - Add, subtract, multiply, divide, and simplify polynomial expressions.

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