Unit 4:
Modeling Polynomial Functions
AA.FGR.5: Extend exploration of quadratic solutions to include real and non-real numbers and explore how these numbers behave under familiar operations and within real-world situations; create polynomial expressions, solve polynomial equations, graph polynomial functions, and model realworld phenomena.
Learning Goal:
- I can define an imaginary number as the square roots of negative numbers.
- I can write equivalent polynomial expressions involving scenarios using real and complex numbers.
- I can perform operations with pure imaginary numbers or complex numbers.
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Learning Goal:
- I can construct a polynomial regression equation to model between two quantities. [quadratic, cubic, quartic]
- I can create, solve, and graph problems involving situations that model polynomial functions. [quadratic, cubic, quartic]
- I can analyze the characteristics of a polynomial function in context.
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Learning Goal:
- I can create, solve, and graph problems involving situations that model a system of quadratic and linear functions.
- I can explain the intersection of linear-quadratic systems as a solution in context.
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Learning Goal:
- I can use the fundamental theorem of algebra to identify the possible maximum number of real and imaginary zeroes in a standard-form polynomial.
- I can verify the actual number of real or complex zeroes in the graph of a polynomial equation.
- I can sketch a graph of polynomial equations in standard form.
- I can analyze the graph of a polynomial’s functions by identifying key characteristics.
- I can construct a graph when the polynomial function is written in factored form.
- I can use the characteristics of a polynomial equation to graph the function.
- I can analyze the characteristics of a polynomial graph.
- I can write a polynomial equation in the factored form given the end behavior and the multiplicity of real or complex zeroes.
- I can write multiple polynomial equations using all the real and complex zeroes in standard form.
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