Practice Quiz #9 Polynomials Accelerated Algebra 2 WGHS Math Dept. & Operations Name: ________________________ Period: ____ Date: ________ You MUST SHOW YOUR WORK in a legible fashion using mathematically correct notation. 1. An architect uses a cylindrical tube to ship blueprints to a client. The height of the tube plus twice its

radius must be less than 120 cm. a. Write an expression for h, the height of the

tube, in terms of r, the radius of the tube.

b. Write an expression for V, the volume of the tube, in terms of r, the radius of the tube.

c. Find the radius that produces the maximum volume.

d. Find the maximum volume of the tube.

2. Sketch the graph of the polynomial function.    𝑓 𝑥 = 𝑥! − 4𝑥! + 4𝑥

Name any x-intercepts, y-intercepts, relative maximums, and relative minimums for the function.

x-intercepts: _______________________ y-intercepts: _______________________ relative maximums: _________________ relative minimums: _________________

3. Describe the end behavior of each function.

a. 𝑓 𝑥 = −𝑥! − 4𝑥! + 5𝑥! + 6 b. 𝑓 𝑥 = !!𝑥! − 6𝑥! − 3𝑥 + 5

4. Identify the type of symmetry associated with each relationship.

a. 𝑓 −𝑥 = −𝑓(𝑥) __________________ b. 𝑓 −𝑥 = 𝑓(𝑥) __________________

5. Is the following function even, odd, or neither? Justify your

answer.

6. Perform the indicated operation. Write your answers in standard form.

a. 3𝑥 − 4+ 𝑥! − (4𝑥! + 7)

b. (−5𝑥! − 2𝑥 + 3)÷ 𝑥 + 3   (via long division)

c. (4𝑥! − 2𝑥 − 2)(2𝑥! + 3𝑥 + 3)  

d. !!!!!!!!!!!!

!!! (via synthetic division)