Module D: Polynomials Review! Grudgeball Module D: Polynomials Review!

Directions: Each group begins the game with 10 X’s. A question will be asked and each team needs to discuss and write their final (simplified) answer on their whiteboard. The team(s) that gets the answer correct gets to remove 1 x from anoth team. Before you take away x’s, you will get to increase the number of x’s by shooting the ball into the bucket. A 2 point shot gets you 2 more x’s, a 3 point shot gets you 3 more x’s. You may not remove x’s from your own team. If your group is eliminated, you may win your way back in by getting an answer correct and shooting a basket (3 or 4 x’s) Winning team has the most x’s left at the end of the game!

# 1 (7a) Find the factored form of the polynomial function that best describes the curves in the following graph. (Use M(x) to describe the curve that looks like the letter M and W(x) to describe the curve that looks like the letter W.)

# 2 (7b) For the polynomial below: find the degree, determine the end behavior, find the zeroes, and the local minimums/maximums.

# 3 (7c) Given -1 ≤ x ≤ 3, what is the difference between the local minimum values of the following functions?  

# 4 (7d) A sheet of metal 12 inches by 10 inches is to be used to make an open box. Squares of equal size are cut out of each corner and then sides are folded up and welded to make a box. What is the maximum volume of the box that can be constructed only using one sheet of metal?

# 5 (8a) Write an equivalent algebraic expression in standard polynomial form: (3x4 + 5x3 – 7x2 + 9x – 1) + (2x4 + 4x2 + 6x + 8)

# 6 (8a) (3x5 + 5x3 – 7x2 + 9x – 1) – (2x4 + 4x3 – 6x + 8) Write an equivalent algebraic expression in standard polynomial form: (3x5 + 5x3 – 7x2 + 9x – 1) – (2x4 + 4x3 – 6x + 8)

# 7 (8a) Write an equivalent algebraic expression in standard polynomial form: (7x2 + 9x – 1)(2x + 3)

# 8 (8b) Divide the following polynomials:

# 9 (8c)

# 10 (8d)

# 11 (9a)

# 12 (9b) Write a rule based on the zeroes for the following polynomial function: A polynomial with zeroes at -2, 0, and 2.

#13 (9c) State if the following binomial (divisor) is a factor of the polynomial without actually dividing:

#14 (10a) Rewrite the following quadratics in all three forms (standard, factored, vertex) and use those forms to reveal it’s key features (x and y-intercept(s) and vertex) without graphing.

#15 (10b)

#16 (10b)

#17 (10c)

#18 (10d)  

#19 (10e) Write the equation of the parabola made with the following conditions: Focus @ (1, 3) Directrix @ y = 1

#20 (10e) Write the equation of the parabola made with the following conditions: Vertex @ (0, 0) Directrix @ y = -2

#20 (7a) Write the equation of the polynomial with the following characteristics: A cubic function with a zero at (1, 0) and a zero at (-3, 0)  multiplicity of 2.

#20 (7b) For the polynomial below: find the degree, determine the end behavior, find the zeroes, and the local minimums/maximums.