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Algebra 2 Name: ____________________ HW#7 Fundamental Theorem of Algebra and Graphs of Polynomial Functions I. 1. Find the requested information for each polynomial graph. All polynomials are in standard form. P x 4 x 4 3x3 x 2 4 2. P x 2 x 7 6 x5 2 x 3 Leading Coefficient: _________ Leading Coefficient: _________ Degree: _________ Degree: _________ y -intercept: _________ y -intercept: _________ Total Number of Roots: _________ Total Number of Roots: _________ End Behavior: End Behavior: x , y __________ x , y __________ x , y __________ x , y __________ II. Sketch a graph of the function WITHOUT using the graphing calculator. Include real zeros on the graph and the end behavior. Also specify the degree of the polynomial. 5. P x x 2 IV. 8. 2 x 3 x 1 3 6. P x x 2 x 5 2 x 2 Identify whether the following graphed functions have an odd or even degree and also whether they have a positive negative leading coefficient. For the real roots, identify whether positive or negative and their multiplicity. 9. Odd or Even? ________________ Odd or Even? ________________ or Leading Coefficient? ________________ or Leading Coefficient? ________________ Real Roots? ( or AND multiplicity) Real Roots? ( or AND multiplicity) III. Write a possible equation for a polynomial with the following sketch. Leave your equation in factored form. 11. 12. 10. Write the simplest polynomial function (in standard form) with the following zeros. 1. 3i and 5 II. Solve each equation by finding all the roots (EXACT VALUE). Use the calculator to help you. 2. x 7 x 15 x 9 0 3 2 3. x 3x 5 x 27 x 36 4 3 2