NAME:________________________
ALGEBRA 2 HONORS
REVIEW FOR CHAPTER 6 TEST
No Graphing Calculator for problems 1 - 8:
1) Solve the equation by first finding rational roots:
f ( x)  x 4  2 x 2  16x  15
2) Solve the equation a root is given:
f ( x)  x 3  3x 2  x  5, x  2  i
Graph:
3) f ( x)  ( x  2)( x  2) 2
4) f ( x ) 
1
( x  1) 2 ( x  3) 2
3
Factor:
5) 8x 3  27
6) x 3  3x 2  16x  48
7) Write a cubic function that passes through the given points.
A(5,7), B(4,0), C (7,0), D(1,0)
8) Write a polynomial function, with integer coefficients, of least degree that has the
following roots:
1
5,
, 4  3i
2
Use the graphing calculator:
9) f ( x)  x 5  3x 2  4 x
a) Describe the end behavior
b) Find all intercepts.
c) Find all local maximums and local minimums
d) Sketch
10) From 1990 to 1999, the annual sales (in millions of dollars) of a certain company can
be modeled by S  0.4t 3  4.5t 2  9.2t  202 where t is the number of years since 1990.
a) Graph with the graphing calculator
b) Approximate the year in which sales reached a low point.
c) If this polynomial function continues to model the sales of the company in the future,
what can the expected sales be in 2000?
11) You are designing an open box to be made from a piece of cardboard that is 8 inches
by 12 inches. The box will be formed by cutting squares from the corners and folding up
the sides to form a box. You want the box to have the greatest volume possible.
a) Write an equation that represents this information.
b) How many inches should you cut.
c) What is the maximum volume?
d) What are the approximate dimensions of the box?
12) The polynomial function P  0.134 x 3  5.775x 2  70.426 x  481.945 models the
number of points earned by the gold medal winner of the platform diving event in the
summer Olympics, where t is the number of years since 1972. Graph the function and
identify any turning points on the interval
. What real-life meaning do these
points have? (Hint: The Olympics only take place every four years)
13) The table below shows the average price (in thousands of dollars) of a house in the
Northeastern United States for 1987 to 1995. Find a cubic model for the data. Then
predict the average price of a house in the Northeast in 2000.
x 1987 1988 1989 1990 1991 1992 1993 1994 1995
f(x) 140 149 159.6 159 155.9 169 162.9 169 180