Chapter 5—parabolas [vertex (max/min), axis of symmetry, y-intercept, zeros]
solving quadratic equations by square rooting and by factoring
“roots”= “zeros”= “solutions” =“x-intercepts”
work with complex #s ( i )
use quadratic formula; use discriminant to determine #, type of solutions
(We did not do the section on complete the square)
Calculator skills: On graph of parabola, use (2nd) CALC to find max, min,
zeros(entering left bound, right bound); use(2nd) TABLE for zeros;
use i on calculator; quadratic regression(using STAT)
---------------------------------------------------------------------------------------------------------------1. Given f(x) = 2x2 – 8x + 5
a) What is the y-intercept?
b) What is the minimum value?
c) What is the axis of symmetry?
2. For f(x) = (x – 3)2 + 2,
a) What is the vertex?
b) What is the y-intercept?
3. Factor.
a) x2 – 64
b) 3x2 + 5x – 2
c) x2 – 5x – 6
d) 6x2 + 24
4. Use factoring to find the zeros.
a) f(x) = x2 + 6x – 16
b) f(x) = 4x2 – 625
5. Solve the equations:
a) 2x2 = 150
b) x2 + 16 = 0
6. How many real roots does f(x) = 2x2 – 5x + 10 have?
7. Write a quadratic function in standard form that has zeros of –4 and 5.
8. What is the complex conjugate of 6 + 2i ?
9. Multiply: (6 – 2i)(5 + i)
10. Simplify:
11. Use the quadratic formula to find the zeros.
a) f(x) = x2 – 5x + 9
b) f(x) = 2x2 + 4x – 7
12. Use your calculator to determine the equation of a quadratic function that contains
these points: (1, 2) (2,-1) (5,2)
Chapter 6—classify polynomials (special names based on degree and # of terms)
Add, Subtract, Multiply (including binomial expansion (pascal’s ∆), and
Divide Polynomials(synthetic division)
Factor polynomials—GCF, quadratic factoring, factoring by grouping,
factoring sum and difference of 2 cubes
List possible roots for a polynomial function (
)
Find all roots using combination of calculator, synthetic division, factoring
Write a polynomial function given its roots.
Describe end behavior given function & determine odd/even degree and sign
of leading coefficient given graph
Calculator skills: use (2nd) TABLE to locate root(s)
-----------------------------------------------------------------------------------------------------------------1. Classify the polynomial using 2 words describe its # of terms and its degree.
a) 9x3 – 15
b) 2x2 + 5x – 1
Add, subtract or multiply
2. (x3 – 5x2 + 6x + 7) – (2x3 – 4x2 – 8x +9)
3. (4x + 1)(3x2 – 6x + 5)
4. (3x + 2)5
5. Divide (x3 – 4x2 + 3x +2)
6. Divide (2x3 + 6x2 + 5)
(x – 3)
(x + 4)
7. Use synthetic substitution to evaluate P(x) = 3x4 – 6x3 + 5x2 – x + 6 for x = –3
8. Factor completely:
a) 4x3 – 8x2 – x + 2
c) x4 + 8x2 + 12
b) x3 + 64
d) 8x2 – 128
9. List the possible roots for f(x) = 2x5 + 4x4 – 3x2 + 5x – 6
10. Find all of the roots; if root is repeated, state its multiplicity; no rounded decimals!
a) x4 – 12x2 + 27 = 0
b) x3 + 2x2 + x + 2 = 0
c) x3 + 3x2 – 3x – 1 = 0
d) x3 + 3x2 + 3x + 1 = 0
11. Write a polynomial function that has the given roots:
a) –3i and 5
b)
and –4
12. Describe the end behavior for the following functions.
a) P(x) = x5 – 6x4 + 2x3 – 6
b) P(x) = -2x4 – 5x3 + 6x2 – x + 2
as x 
, P(x)  ___________
as x 
, P(x)  ___________
as x 
, P(x)  ___________
as x 
, P(x)  ___________
Chapter 7—work with exponential functions involving growth and decay (“multiplier”)
use compound interest formula
write inverses of functions [f-1(x)]; graph inverses of functions
convert between logarithmic form  exponential form
domain, range and asymptotes
use properties of logarithms…write as a single logarithm, “duh” problems
use change of base formula to calculate logs
solve exponential equations and logarithmic equations
work with problems that involve base e and ln; use A = Pert formula
Calculator skills: adjust WINDOW for growth, decay problems;
accurately evaluate when using formulas; use LOG, LN, e,
(use logBASE if your calculator has it)
------------------------------------------------------------------------------------------------------------------1. Which functions below show an exponential growth function?
f(x) = 4(1.4)x
f(x) = 0.5
2. Write the inverse for each function.
a) f(x) = 4x – 5
f(x) = 2x
f(x) = 1.2x2
f(x) = 6
b) f(x) = (x + 3)
3. A computer’s value starts at $4000 and decreases by 8% each year.
a) Write a function A(t) to represent the value of the computer as a function of t
years.
b) What is the multiplier?
c) Find the value of the computer after 5 years.
4. A population of bacteria starts at 500 and doubles every hour.
a) Write a function A(t) to describe the amount of bacteria as a function of t hours.
b) What is the multiplier?
c) Find the amount of bacteria after 8 hours.
5. The population of Hornetville was 7500 in 2008 and has been increasing at a rate of
3.6% per year.
a) Write a function A(t) to describe the population as a function of t years.
b)What is the multiplier?
c) If the population increases at the same rate each year, in what year would we expect
the population to exceed 15,000?
6. Write in exponential form
a)
=6
b) log (0.001) = –3
c) ln x = 4
b)
c)
7. Write in logarithmic form
a)
= 0.04
= 216
8. Give the domain and range and asymptote for f(x) = 3x
9. Give the domain, range and asymptote for f(x) =
=5
10. Write as a single logarithm; then simplify.
a)
+
b)
–
c)
–
0
d) ln 0.5 + ln 2
11. Write
as a product (write without the exponent)
12. Calculate to the nearest tenth:
a)
13.
b)
c) ln 10
b)
c) ln
Simplify:
a)
14. Solve the equations
a)
= 40
d) 2
–
=0
b)
c)
+
=
=8
e)
=3
f) ln 5 + ln x = 6
15. Calculate the amount of money you’d have after 5 years if you invest $10,000 at 3.5%
in an account that compounds continuously. (A = Pert)
Chapter 8—direct variation, inverse variation, and joint variation
-determine if data represents direct, inverse or neither
-solve problems using equations y = kx OR y =
-graphs of direct variation, inverse variation
Rational expressions…..simplify, add/subtract, multiply/divide
Simplify complex fractions
Solve rational equations
Identify zeros, vertical asymptotes, horizontal asymptotes, holes, domain, and
range of rational functions
Simplify radical expressions including
, and
Understand rational exponents (exponents that are fractions)
Identify domain and range of radical functions; graphs of radical functions
Solve radical equations
Calculator skills: working with graphs of rational functions;
calculating square roots, cube roots, 4th roots, etc.
-----------------------------------------------------------------------------------------------------------------1. If w varies inversely as h and w = 5 when h = 4, write the equation that describes
this relationship.
2. The lateral surface area (L) of a cone varies jointly as the base radius r and the slant
height l . If L = 63 when r = 3.5 and l = 18. Find r when L = 8 and l = 5.
3. Determine if the data set represents direct variation, inverse variation, or neither.
a)
b)
x 8 4 2 1
y 12 6 4 2
x
y
2
5
10 12
1.5 0.6 0.3 0.25
4. If y varies directly as x, with a constant of variation equal to -2, graph the function.
5. Add, subtract, multiply or divide:
a)
+
b)
6. Simplify
c)
·
7. Identify the zero(s) and vertical asymptote(s) for f(x) =
8. Give the domain and range for f(x) =
–3
9. What is the horizontal asymptote for f(x) =
10. Where is the hole in the graph of f(x) =
11.
a)
?
?
Solve.
=
b)
= +2
c)
=
12.
Simplify
a)
c)
b)
13.
Which of these is not equal to the others?
14.
Describe 3 ways that f(x) = 6
15.
Give the domain and range of f(x) =
Solve.
a) 6
+ 5 is transformed compared to f(x) =
2
16.
b) 3
=
= 42
c)
=
Chapter 11 –calculate the number of possible outcomes using the fundamental counting
principle
understand factorial (!) and simple permutations
find probabilities involving rolling a die, drawing a card from a deck, etc.
find probability of “not A”
-----------------------------------------------------------------------------------------------------------------1. Sally wants to make a sandwich. She can choose 1 type of bread with choices white,
rye or wheat; 1 meat with choices ham, turkey, beef, or salami; and 1 cheese with
choices cheddar, swiss, or provolone. How many different possible sandwich
combinations are there?
2. How many different 7-digit phone numbers are possible if the first digit cannot be 0
or 1?
3. How many 3-digit PINs are possible, if there are no restrictions on the numbers that
can be used for each digit?
4. How many different ways can the letters in the word HINSDALE be arranged?
5. There are 10 players on the team. How many possible ways can a captain and cocaptain be chosen?
6. How many ways can a 15-member club choose their President, Vice President,
Secretary and Treasurer?
7. A standard 6-sided die is rolled. Find:
a) P(4)
b) P(odd)
c) P(not 6)
8. A card is drawn from a standard 52-card deck. Find:
a) P(spade)
b) P(red)
c) P(Ace of Hearts)
9. The animal shelter has 40 cats and dogs. Timmy counted 26 cats. If an animal is
chosen at random what is the probability that it is a dog?
10. A poker chip is chosen at random from a box containing 10 green, 20 blue, and 6
black. Find:
a) P(blue)
b) P(red)
c) P(not black)
GRAPHS
1. a)What do you know about the zeros of the function graphed below?
b)What do you know about the discriminant of this function?
2. Determine if the functions graphed below have
DEGREE that is odd or even and
LEADING COEFFICIENT that is + or –
3. Which of the following is the graph of f(x) = ex ?
4. Which graph shows the inverse variation function y =
?
5. Match the function to its graph.
f(x) =
f(x) =
+2
f(x) =
f(x) =