Trashketball Review Chapter 6 Polynomial Functions and Stuff

11 2 3 4 5 Trashketball Review of ch 3 6 11 16 21 26 7 12 17 22 8 13 18 23 9 14 19 24 10 25 15 20

3 F(x) =

4 Using your TI-83, identify the xintercepts, local max and local min of the graph of X-int: (0, -3) and (0, 3)

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8 Find all of the zeros of the function below:

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10 Create a function for the following end behavior. The function must be of degree 5 or higher and the function must have at least 5 terms. Answers will vary but MUST be correct to get credit.

11 Use synthetic division to determine if 2 is a zero of f(x) = 2 x 3 – 3 x 2 – 6 x + 6. And EXPLAIN how you know. No. f(2) has a remainder of -2

12 Suppose a polynomial function of degree 5 with rational coefficients has the given zeros: -3, , and 4+3 i. Find the other zeros.

13 Use synthetic substitution to find the function value f(-10) if f(x) = x 5 – 4 x 4 + x 3 – x 2 + 2 x - 100

14 Consider the graph the polynomial function: f(x) = 3 x(x + 5)(x – 4)(x + 1)(x – 2): a) What are the zeros of the function? b) What are the x-intercepts of the function? c) What is the degree of this function? a) 0, -5, 4, -1, 2 b) (0, 0), (-5, 0) , (4, 0), (-1, 0) , (2, 0) c) 5 th degree

15 Use synthetic division to find the 4 2 quotient (x - 6 x + 5) ÷ (x + 3) x 3 – 3 x 2 + 3 x – 9 +

16 Find ALL zeros of the function f(x) = 4 x + 3 x – 2, 1, -3 2 7 x –x+6

17 Find a polynomial of lowest degree with rational coefficients that has the given numbers as some of its zeros: 3, 2 – 5 i

18 Mathematically describe the end behaviors for the function below: f(x) = 6 x 3 – 2 x 2 – 5 x 8 + 3 x - 9 Must have both parts correct:

19 List all possible rational zeros of the function f(x) = 3 9 x – 2 5 x + x – 12

20 Simplify

g(x) = 21 Multiply: (x+3)(x+2)(x-1) X 3 + 4 x 2 + x - 6

22 For 1990 to 1998, the value of a horse winning the Kentucky Derby can be modeled by: V = 2553 x 3 – 25200. 56 x 2 + 64026. 95 x + 428075. 56 Where x is the number of years since 1990. Use a graphing calculator to determine what year the winnings were $488, 150

23 There are seven teams in the Atlantic Division of the Eastern Conference of the NBA. During the 1997 -98 season the winning percentage of teams in this division can be modeled by: W = -0. 0051 x 3 + 0. 063 x 2 – 0. 260 x + 0. 862 Where x is the team’s ranking within the division. Orlando’s winning percent was 0. 500. Use the graphing calculator to estimate their ranking in the division. 5

24 Write a cubic function that passes through the given points: (-1, 0), (2, 0), (3, 0), (0, 9) f(x) = 3/2 (x+1)(x-2)(x-3)

25 Factor: x 4 - 16 2 (x + 4)(x + 2)(x – 2)

26 Solve: x 3 + 4 x 2 = 7 x + 28