Page 55 - Mathematics_Form_3

Functions

corresponding value of . Use
4( − 2 ) (4 ) − ( − 3) 41
2
_

= ______________ = the curve to solve the following
4( − 2) 8
41 equations:
_
Thus, y = .
8 (a) x − 4x − 2 = 0
2
41
_
Therefore, the maximum value is .
FOR ONLINE READING ONLY
2
8 (b) x − 4x + 3 = 0
An alternative way of finding the (c) x − 3x − 40=
2
maximum value is by completing the In questions 3 to 5, write the functions
square: in the form of y = a (x + b) + c, where
2
2
y = − 2 x − 3x + 4 , , and are constants.
3 _
= − 2 x + x + 4 3 . y = x + 8x + 5
2
(
)
2
2
Completing the square, gives
2
2 4 . y = 3 x + 8x − 1
9 _
3 _
y = − 2 x + + 4 + 5 . y = 5 − 6x − 9 x
(
)
4
8
2
2
41
y = − 2 x + + In questions 6 to 9, find the maximum
3 _
_
)
(
4 8
41
Therefore, the maximum value is . or minimum value and the axis of
_
8 symmetry:
2
6 . y = x − 8x + 18
Exercise 2.5
2
7 . y = 1 + 6x − 3 x
1. Draw the graph of a function 8 . y = 2 x + 3x + 1
2
f (x ) = x − 6x + 5. Find the 2
2
minimum value of this function 9 . y = 2 − x − x
and the corresponding value of . 10. Given the function f (x ) = 2x − x ,
2
2. Draw the graph of the function find its maximum or minimum
Mathematics for Secondary Schools Step functions
y = x − 4x + 2. Find the minimum
value and the axis of symmetry.
2
value of the function and the
A step function is a function that changes in jumps, not in a smooth line. It stays
constant over certain intervals and then suddenly changes to a new value. The
graph of a step function looks like a series of horizontal steps, thats why it is
called step function. An example of a step function is the cost of posting parcels,
where the price increases in steps depending on the weight range as shown in the
following table.
(mass in

grams) 0 < x ≤ 1 1 < x ≤ 2 2 < x ≤ 3 3 < x ≤ 4 4 < x ≤ 5
y (cost in 150 200 250 300 350
Tsh)
48 Student\s Book Form Three
18/09/2025 09:58:58
MATHEMATIC F3 SB.indd 48
MATHEMATIC F3 SB.indd 48 18/09/2025 09:58:58