Page 3 - 1202 Question Bank Mathematics Form 4

MUST

KNOW Important Facts

Quadratic Expressions and Functions Sketching the Graph of a Quadratic Functions

1. The general form of the quadratic expression is ax + bx + c For example, f(x) = 2x + 5x – 12
2
2
with a, b and c are constants and a ≠ 0. Step 1: When a = 2 . 0, the shape
2. The highest power of the quadratic expression is 2 and Step 2: When c = –12, y-intercept = –12
involved only one variable. Step 3: When f(x) = 0
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3. The general form of the quadratic functions is 2x + 5x – 12 = 0
2
f(x) = ax + bx + c.
2
4. For a graph of quadratic function f(x) = ax + bx + c, (2x – 3)(x + 4) = 0
2
3
When a . 0, When a , 0, x = or x = – 4
2
f(x) f(x)
x = m x = m f(x)
2
y = ax + bx + c (m, n)
n
c
x x x
c 0 0 0 3
n (–4, 0) (–, 0)
2
(m, n) y = ax + bx + c 2

• Curved graph: . • Curved graph: . (0, –12)
• Minimum point: (m, n) • Maximum point, (m, n)
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Values of a, b and c on Quadratic Functions Number Bases
When a . 0, 1. Digits used in base two up to base ten:
The value of a y y y Number base Digit
determines the Base 2 0, 1
shape of graph 0 x 0 x 0 x Base 3 0, 1, 2
b < 0 b = 0 b > 0 Base 4 0, 1, 2, 3
Base 5 0, 1, 2, 3, 4
When a , 0,
The value of b y y y Base 6 0, 1, 2, 3, 4, 5
determines the Base 7 0, 1, 2, 3, 4, 5, 6
position of the 0 x 0 x 0 x Base 8 0, 1, 2, 3, 4, 5, 6, 7
Base 9
axis of symmetry b < 0 b = 0 b > 0 Base 10 0, 1, 2, 3, 4, 5, 6, 7, 8
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
2
When a . 0 When a , 0 2. For 2431 → Place value = 5 = 5 × 5 = 25
5
The value of Digit value = 4 × 5 = 4 × 25 = 100
2
c determines y y Number 2 4 3 1
the position of c c Place value 5 3 5 2 5 1 5 0
y-intercept. x x Digit value 250 100 15 1
0 0
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Roots of a Quadratic Equation Conversion of Number Bases
1. The roots of a quadratic y 1. To convert a number in a certain base to base ten
equation ax + bx + c = 0 are 172 = (1 × 8 )+ (7 × 8 ) + (2 × 8 )
2
1
2
0
the points of intersection of Root 4 Root 8 = 64 + 56 + 2
the graph and the x-axis. 2 x = 122
2. The roots of the quadratic –2 –1 0 1 2 3 4 10
–2
equation can be determined by: –4 2. To convert a number in a base ten to certain base
(b) 234 to base eight
(a) 123 to base five
(a) Factorisation method: 10 10
x + 5x + 6 = 0 5 123 8 234
2
(x + 3)(x + 2) = 0 5 24 –3 8 29 –2
Thus, the roots are –3 and –2. 5 4 – 4 8 3 –5
(b) Graphical method: 0 – 4 0 –3
Step 1: Determine the shape of the graph by identifying º 123 = 443 5 º 234 = 352 8
10
10
the value of a. 3. To convert a number in a certain base (not base ten) to
Step 2: Determine the y-intercept another base (not base ten)
Step 3: Determine the x-intercept
Base p Base 10 Base q
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Must Know 1202QB Maths Form 4.indd 1 21/02/2022 10:48 AM