2.3
Solving Quadratic Equations
The process of completing the square, which was used
in Section 2.2 to find the maximum or minimum of
a quadratic function, is also one of the ways to solve
quadratic equations.
In Roman times, a city forum was a large open

3.3
Horizontal and Vertical
Translations of Functions
When an object is dropped from the top of a bridge
over a body of water, the approximate height of the
falling object above the water is given by the function
h(t) 5t2 d
where h(t) metres is the height

1.3
Solving Exponential Equations
Radioactive isotopes have many uses, including medical diagnoses
and treatments, and the production of nuclear energy.
Different radioactive isotopes decay at different rates. The time
it takes for half of any sample of a

6.4
Recursion
Formulas
In previous sections, you have
determined sequences using a formula
for the nth term. An example is the
formulan t 2n 3 or f(n) 2n 3,
which determines the arithmetic
sequence 5, 7, 9, 11, 13,
Another example is the formula
tn 2n 1

3.5
Inverse Functions
x 1
Inverse functions are a special class of
f(x) 2x 1
g(x)
2
functions that undo each other. The input
Input, x Output, f (x) Input, x Output, g(x)
and output values for two inverse functions,
0
1
1
0
x 1
f(x) 2x 1 and g(x)
, are sh

3.4
Reflections of Functions
y
A
A coordinate grid is superimposed on a cross section of the Great
Pyramid, so that the y-axis passes through the vertex of the pyramid.
The x-axis bisects two opposite sides of the square base.B The two
sloping lines in th

3.1
Functions
Cubic packages with edge lengths of 6 cm,
3
7 cm, and 8 cm have volumes
or of 6
3
3
3
216 cm
, 73 or 343 cm
, and 38or 512 cm
.
These values can be written as a relation,
which is a set of ordered pairs, (x, y). The
relation is cfw_(6, 216),

1.7
Adding and Subtracting Rational Expressions, I
The blimp that provided overhead television
coverage of the first World Series played in
Canada was based in Miami. The blimp flew
1610 km from Miami to Washington, D.C.,
and then 634 km to Toronto.
The t

3.2
Investigation: Properties of Functions
1
Defined by f(x) =x and f(x) =
x
Properties of the Function
xf(x) =
Recall that f(x) is another name for y.
0
1
4
9
16
the function
xy manually by x
y
copying and completing the table of values,
or graph the fu

5.6
Translations and Combinations
of Transformations
The highest tides in the world are found in the
Bay of Fundy. Tides in one area of the bay cause
the water level to rise to 6 m above average sea
level and to drop to 6 m below average sea level.
The ti

1.2
Rational
Exponents
Most of the power used to move a
ship is needed to push along the bow
wave that builds up in front of the
ship. Ships are designed to use as little
power as possible.
To ensure that the design of a ship is
energy-efficient, designer

1.9
Solving First-Degree Inequalities
Canadian long-track speed skater Catriona LeMay
Doan broke world records in both the 500-m and the
1000-m events on the same day in Calgary.
Event
Catrionas TimeOld
(s) World Record (s)
500-m
1000-m
37.90
76.07
38.69

1.8
Adding and Subtracting Rational
Expressions, II
The three-toed sloth of South America moves very slowly. It can travel twice as fast
in a tree as it can on the ground. If its speed on the ground is s metres per minute,
its speed in a tree is 2s metres

2.2
Maximum or Minimum of a Quadratic
Function by Completing the Square
To celebrate Canada Day and Independence Day,
the International Freedom Festival is held at the
end of June in Windsor, Ontario, and Detroit,
Michigan. At the end of the festival, the

1.1
Reviewing the Exponent Laws
I NVESTIGATE & I
NQUIRE
An order of magnitude is an approximate size of a
quantity, expressed as a power of 10.
The table shows some speeds in metres per
second, expressed to the nearest order of
magnitude.
Entity
Speed (m/

3.6
Stretches of Functions
The clock in the Heritage Hall clock tower, in
Vancouver, is known as Little Ben. It was built by
the same company that built Big Ben in London,
England. Little Ben is a mechanical clock with a
pendulum.
On the Earth, the period

2.5
Operations With Complex
Numbers in Rectangular Form
The computer-generated image shown is called a
fractal. Fractals are used in many ways, such as
making realistic computer images for movies and
squeezing high definition television (HDTV)
signals int

1.6
Multiplying and Dividing Rational Expressions
The game of badminton originated in England
around 1870. Badminton is named after the
Duke of Beauforts home, Badminton House,
where the game was first played. The
International Badminton Federation now ha

3.7
Combinations of Transformations
Because of its mathematical
simplicity, the 3-4-5 right
triangle has as much appeal
today as it did thousands of
years ago. In architecture, a
3-4-5 right triangle, with 4 as
the base, has a hypotenuse with
the slope of

5.8
Trigonometric Equations
To calculate the angle at which a curved section of
highway should be banked, an engineer uses the
2
equation tan
x v
, where x is the angle of the
224 000
bank and v is the speed limit on the curve, in kilometres
per hour.
2

5.7
Trigonometric Identities
When a ball is kicked from the ground, the maximum height
the ball will reach can be determined by the formula
v02sin2 x
h
.
2g
In this formula, h metres is the maximum height that the ball
will reach,0 metres
v
per second is

2.1 The Complex Number System
The approximate speed of a car prior to an
accident can be found using the length of the
tire marks left by the car after the brakes have
121d
been applied. The formula
s gives the
speed, s, in kilometres per hour, where d i

6.3
Geometric Sequences
In the sequence 2, 10, 50, 250, , each term after the
first is found by multiplying the preceding term by 5.
Therefore, the ratio of consecutive terms is a constant.
10
5
2
50
5
10
250
5
50
This type of sequence is called a geometr

6.2
Arithmetic Sequences
A sequence like 2, 5, 8, 11, , where the difference
between consecutive terms is a constant, is called an
arithmetic sequence. In an arithmetic sequence, the
first term,
, tis denoted by the letter a. Each term
1
after the first i

4.3
The Sine Law and
the Cosine Law
The Peace Tower is the tallest part of Canadas
Parliament Buildings. A bronze mast, which
flies the Canadian flag, stands on top of the
Peace Tower.
From a point 25 m from the foot of the tower,
the angle of elevation o

5.2
Trigonometric Ratios of Any Angle
The use of cranes to lift heavy objects is an essential
part of the construction and shipping industries.
There are many different designs of crane, but they
usually include some kind of winding mechanism,
called a wi

4.4
The Sine Law: The Ambiguous Case
Canada has 1.3 million square kilometres of
wetlands, or almost 25% of all the wetlands in the
world. These marshes and swamps help to prevent
flooding and act as natural water purifiers.
Wetlands provide a habitat for

5.1
Radians and Angle Measure
To describe the positions of places on the Earth,
cartographers use a grid of circles that are north-south
and east-west. The circles through the poles are called
meridians of longitude. The circles parallel to the
equator ar

1.5
Simplifying Rational Expressions
Canada officially has two national games, lacrosse
and hockey. Lacrosse is thought to have originated
with the Algonquin tribes in the St. Lawrence
Valley. The game was very popular in the late
nineteenth century and w

4.2
The Sine and the Cosine of
Angles Greater Than 90
The trigonometric ratios have been defined in terms of sides
and acute
y
angles of right triangles. Trigonometric ratios can also be defined for
angles in standard position on a coordinate grid.
is in

4.1
Reviewing the Trigonometry of Right Triangles
I NVESTIGATE & I
NQUIRE
In the short story The Musgrave Ritual, Sherlock
Holmes found the solution to a mystery at a
certain point. To find the point, he had to start
near the stump of an elm tree and take

2.4
Tools for Operating
With Complex
Numbers
Solar cells are attached to the surfaces of
satellites. The cells convert the energy of
sunlight to electrical energy. Solar cells are
made in various shapes to cover most of the
surface area of satellites.
I N

6.1
Sequences
A number sequence is a set of numbers, usually separated by
commas, arranged in an order. The first term is referred to
as 1t, the second term
, as
thet third term3,as
and
t so on.
2
The nth term is referred nto
. as t
A sequence may stop at

1.4
Review: Adding, Subtracting, and
Multiplying Polynomials
Key Concepts
To add polynomials, collect like terms.
To subtract polynomials, add the opposite.
To multiply a polynomial by a monomial, use the distributive property
to multiply each term in