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## Click here for Parent Guide with Extra Practice for Chapter 8 - Polynomials from CPM

 Chapter Objective Students will be able to… Standard(s) Help/Examples Practice 8.1.1 Describe the graph of a polynomial given its equation in factored form A-APR.3 F-IF.4 F-IF.7c Polynomial end behaviorPolynomial end behavior example 8.1.2 Consolidate, generalize the graph of a polynomial given its equation in factored form A-APR.3 F-IF.7c Determine the x-intercepts of a polynomial function by analyzing its factorsDetermine the end behavior of a graph by analyzing its equationDetermine when a polynomial function changes signSketch the graph of a higher degree polynomialDetermine the equation of a polynomial by analyzing its graph 8.1.3 Write exact equations for the graphs of polynomial functions given the x‑intercepts and one additional point A-APR.3 F-IF.4 F-IF.7c Writing Polynomial Equations given the Zeros of the Functions 8.2.1 Solve equations using imaginary and complex numbers N-CN.1 N-CN.7 N-CN.9 (+) Introduction to i and imaginary numbersImaginary roots of negative numbersIntroduction to complex numbers https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/e/the-imaginary-unit-and-complex-numbers 8.2.2 Write the equations for quadratic functions given the roots N-CN.1 N-CN.7 N-CN.8 (+) N-CN.9 (+) Write a Polynomial Function with Complex Zeros 8.2.2 Practice operations with complex numbers N-CN.2 Calculating i raised to arbitrary exponentsAdding complex numbersSubtracting complex numbersMultiplying complex numbersDividing complex numbers Imaginary unit powersAdding and subtracting complex numbersMultiplying complex numbersDividing complex numbers 8.2.3 Use the complex plane as a way to visualize complex numbers and complex roots for quadratic functions N-CN.1 N-CN.7 N-CN.9 (+) Plotting complex numbers on the complex plane 8.2.3 Calculate the absolute value of a complex number N-CN.2 Absolute value of a complex number Absolute value of complex numbers 8.3.1 use polynomial division to find factors of polynomials A-APR.2 A-APR.6 N-CN.9 (+) Polynomial divisionDividing polynomials 1Dividing polynomials with remaindersSynthetic divisionSynthetic division example 2 8.3.2 Use the Integral Zero Theorem, polynomial division and the Factor Theorem to find integral roots and to find all roots of polynomials with degree greater than two A-SSE.2 A-APR.2 A-APR.3 A-APR.6 F-IF.7c N-CN.8 (+) N-CN.9 (+) Example: Factoring a fourth degree expressionFactoring 5th degree polynomial to find real zerosIdentifying graph based on roots Using zeros to graph polynomials 8.3.3 Use knowledge of polynomial functions and graphs to maximize volume of a tank A-APR.2 A-APR.3 A-APR.6 F-IF.5 F-IF.7c N-CN.9 (+)