Page 71 - Mathematics_Form_Two

Algebra

For example, in the quadratic expression
1
8. V = p rh r 4x − 2 6x + 7, the coefficient of x is 4, the
2
2
2
coefficient of x is 6− and the constant is
1
9. S = at 2 t 7.
2
1 1 1 Activity 4�2: Deducing quadratic
FOR ONLINE READING ONLY
10. = + f
f u v expressions from real
life
æ 1 a+ ö 1. A garden designer plans to design
11. P w = ç ÷ a
è 1 a- ø different gardens in a compound. Mathematics for Secondary Schools
During an investigation, he noticed
l
12. T = 2p g that the length of each garden is 4
g m longer than its width. Deduce the

5 simplest possible expression of the
13. C (F = - 32 ) F
9 area of the garden by expanding the
factors.

Quadratic expressions 2. Explore various sources to learn
more about how you can expand
An expression whose highest exponent such results.
(degree) of the variable is 2 is called a
quadratic expression. 3. Make a presentation to demonstrate
how you arrived at your conclusion.
The following are examples of quadratic
expressions:
From activity 4.2, it can be observed that,
(i) 4z + the highest exponent (or quadratic expressions can be derived from
2
3,
degree) of z is 2. the product of two linear expressions. For
(ii) 6y + , y the highest exponent of y instance in Figure 4.1, if the width of a
2
is 2. rectangle is (y + 1) unit and its length is
(2y + 3) unit, then the area is (2y + 3) (y + 1)
(iii) 3n 2 2n - + 1, the highest exponent of square units.
n is 2.
In general, a quadratic expression has the
2
form ax + bx + c, where a ≠ 0 and a, b,
and c are real numbers. The term ax is
2
called the quadratic term, where a is the
2
coefficient of x . The term bx is called the
linear term (middle term), where b is the Figure 4�1: Rectangle PQRS which demonstrate
coefficient of x and c is the constant term. an area as a product of factors

65
Student's Book Form Two

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MATHEMATIC F2 v5.indd 65