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Unit 3 Lesson 1 Quiz Name:____________________________ Form C 1. Suppose a new animated movie will feature a main character that is a two-humped camel. The graph below indicates the shape of the camel’s humps. a. Explain why it is reasonable to use a fourth-degree (quartic) polynomial to model this curve. b. When trying to find a polynomial function rule that would closely match the graph, Dawn began with f(x) = (x – 1)(x – 5)(x + 3)(x + 1). i. Explain why this function rule is a reasonable first choice. ii. How do the shape, zeroes, and end behavior of the graph of f(x) compare to those of the graph above? c. Provide a reasonable set of control points that could be used to find a rule that matches this graph. Explain why you chose the points you did. 2. Use the method of undetermined coefficients to find a quadratic function whose graph passes through the points (–1, 0), (2, 12), and (4, –2). 3. Consider the polynomial p(x) = ((x + 3)x – 15)x + 12 written in nested multiplication form. a. What is the y-intercept of p(x)? b. Rewrite p(x) in standard polynomial form. c. Describe the end behavior of p(x). 4. Consider the polynomial p(x) = π 3 + 2π 2 − 6π − 9 a. Is (x +3) a factor of p(x)? b. Divide p(x) by the linear term (x - 2) and express the result as an equation in the form p(x) = f(x)q(x) + r(x). 5. Write each expression as a product of linear factors. a. ππΏπ − πππΏ + π b. πππ + ππ − π