Honors Pre-Calculus Mrs. Kitchen Folder # ______ Name ______________PolynomialsTest Date ______________

1. MAXIMUM REVENUE The total revenue R earned (in dollars) from production a gift box of candles is given by R(p) = -10p2+ 800p, where p is the price per unit (in dollars).

a) Find the revenues when the prices per box are $20, $25, and $30.

b) Find the unit price that will yield a maximum revenue. What is the maximum revenue? Use complete sentences.

3. Given h(x) = -x7+ 8x2-8x a) Describe the right-hand and left-hand behavior.

As x→∞ , f ( x )→_____ As x→−∞ , f ( x )→_____b)

Is the graph one-to-one?

DATA ANALYSIS: SALES The sales y (in billions of dollars) For Harley-Davidson from 2000 through 2007 are shown intable. (Source: U.S. Harley-Davidson, Inc)

5. NUMERICAL AND GRAPHICAL ANALYSIS An open box is to be made from a square piece of material,

2. Write the equation of the graph in vertex form.

Create a scatter plot of the data. Find a quadratic regression model for the data.

a) How well doe the model fit the data? (Strong or weak)

b) Approximate the time period in which the sales for Harley-Davidson were the greatest to two decimal places.

c) Use the model to predict the sales for Harley-Davidson in 2010.

Honors Pre-Calculus Mrs. Kitchen Folder # ______ Name ______________PolynomialsTest Date ______________

36 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides.

a) Write the function V(x) that represents the volume of the box.

b) Determine the domain of the function.

c) Use your graphing calculator to estimate the value of x for which V(x) is maximum.

6. Determine the polynomial function corresponding to the graph. Leave your answer in factored form.

7. The volume of air flowing into the lungs during a breath can be represented by the polynomial function

V(t) = -0.041t3 + 0.181t2 + 0.202t, where V is the volume in liters and t is the time in seconds.

a) Use a graphing calculator to graph V(t). State your window settings.X min = _____ Y min = _____

X max = _____ Y max = _____

b) What is the maximum volume of air inhaled into the lung?

At what time during the breath does this occur?

c) How many seconds does it take for one complete breath?

d) What percentage of the breath is spent inhaling?

Sketch a graph of each function below. Be sure to identify the type, and to label the roots, and the y-intercept in your sketches.

8) f ( x )=−3 x2( 4−x )2(2 x+5) 9) f ( x )=(x−3)2 ( x−1)3 ( x+4 )

(3,1)

Honors Pre-Calculus Mrs. Kitchen Folder # ______ Name ______________PolynomialsTest Date ______________

10) Which of the following equations best describes the graph shown below?

A) B)

C) D)

11) What is the y-intercept of the graph of ?

A) B) C) D) E)

12) What is the multiplicity of the zero in ?

A) 1 B) 2 C) 3 D) 5 E) 7

13. Given f(x) = x2 - 8x + 19

a) Put the equation into vertex form

Honors Pre-Calculus Mrs. Kitchen Folder # ______ Name ______________PolynomialsTest Date ______________

b) Graph the function.

14. Sketch a graph of a polynomial with the given zeros and corresponding multiplicities. Answers will vary.

x = -5 of multiplicity 3

x = -3 of multiplicity 2

x = 1, of multiplicity 1

x = 4, of multiplicity 2