Page 9 - Spotlight A+ Form 4 & 5 Mathematics KSSM

Form
4
Chapter 1 Quadratic Functions and Equations in One Variable Mathematics
1.1 Quadratic Functions and (c) The expression 6t + pt – 9 contains two CHAP.
2
2
Equations variables p and t. Therefore, 6t + pt – 9 is not 1
a quadratic expression in one variable.
1
—
2
(d) The expression y – 7y contains one variable
Identify and describe the characteristics of 1
—
quadratic expressions in one variable y. However, the power of y in the term 7y is
2
1
—
2
1. Quadratic expression in one variable is an not a whole number. Therefore, y – 7y is not
algebraic expression of the form ax + bx + c, a, b a quadratic expression in one variable.
2
and c are constants, a ≠ 0 and x is a variable. Try question 2 in Formative Zone 1.1
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2. Characteristics of quadratic expressions in one
variable:
• Expressions contain only one variable.
• The power of the variable is a whole number.
• The highest power of the variable is 2. Quadratic equations in one variable
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BRILLIANT Tips
The variable x in quadratic expressions can also be
represented by other alphabet letters. BRILLIANT Tips

If p represents a constant, then 6t + pt – 9 is a
2
Example 1 quadratic expression in one variable, t.
r
2
5
2
2
2
4a + b + 3 — – 2r –h + 8h – 2 3t + —
2 t
Recognise quadratic function as many-
Identify quadratic expressions in one variable
from the list of expressions above. to-one relation, hence, describe the
Solution: characteristics of quadratic functions
r 2 1. Quadratic function is a many-to-one relation.
— – 2r, –h + 8h – 2
2
2 2. Characteristics of quadratic functions
Try question 1 in Formative Zone 1.1 • The graph has a curved shape.
• It has a maximum point or a minimum point.
Example 2
• The axis of symmetry of the graph is parallel
Determine whether each of the following to the y-axis.
expressions is a quadratic expression in one
variable. Give your justification.
2
(a) 2m – 9m + 5 BRILLIANT Tips
(b) 5x – 2x + 10
3
2
(c) 6t + pt – 9 Graphs of quadratic functions y = ax + bx + c
2
1 —
(d) y – 7y 2
Solution: a . 0 a , 0
2
(a) The expression 2m – 9m + 5 contains one Maximum point
variable m and the highest power of m is
2. Therefore, 2m – 9m + 5 is a quadratic Minimum point
2
expression in one variable.
3
(b) The expression 5x – 2x + 10 contains one
Axis of symmetry Axis of symmetry
variable x. However, the highest power of x is
3
3. Therefore, 5x – 2x + 10 is not a quadratic
expression in one variable.
1.1.1 1.1.2 3

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