Page 23 - Ranger SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 2 Quadratic Functions
9. The quadratic function f(x) = hx – 3x + k, 16. The diagram below shows a graph of a
2
where h and k are constants, has one quadratic function.
maximum point.
(a) Given h is an integer such that f(x)
–2  h  2, state the value of h. 8
(b) Using the answer in (a), find the 6
range of values of k when the curve x
of the quadratic function intersects
Form 4 the x-axis at two different points. 17. Given a quadratic function Reserved.
0
9
3
–
2
2

10. Given x – y = 3x, find the range of
2
vertex form, f(x) = a(x – h) + k.
2
values of x for y  4. Express the quadratic function in the
Penerbitan Pelangi Sdn Bhd. All Rights
11. Given 4 is one of the roots of the
2
quadratic equation (x – p) = 169, where f(x) = 3(x – 2) – 5 where a = 3, h = 2 and
2
p is a constant. Find the values of p. k = –5. If the graph of f(x) is reflected
in the x-axis, state the changes in the
12. Given a quadratic equation values of a, h and k.
ax + bx + c = 0, where a, b and c are 18. Given the equation 2x + 8x + 5 = 0 has
2
2
constants, has roots β and 3β. Express c roots p and q. Form a quadratic equation
in terms of a and b.
with the roots 2p + 3 and 2q + 3.
13. Given that straight line y = 6x + 1 does 19. Given a function f(x) = x – (1 – k)x + 1,
2
not intersect the curve f(x) = (2k – 3)x where k is a constant, is always negative
2
+ 4x – 6, where k is a constant. Find the when p  k  q. Find the value of p
range of values of k. and of q.
14. The diagram below shows the graph of Paper 2
5

f(x) = 8 x + 3  2 + . 1. The diagram below shows the graph of a
2
4
f(x) quadratic function f(x) which intersects
the x-axis at the origin and (4, 0).
c f(x)
x
0
x
0 4
Calculate the value of c.
15. Express f(x) = –2x – 6x + 9 in the (a) Find the value of a and of h when
2
form a(x – h) + k where a, h and k f(x) is expressed in the form of
2
are constants. Hence, determine the a(x – h) + 5.
2
maximum value or minimum value and (b) Hence, find the range of values of x
the corresponding value of x. 1
if f(x)  –56 .
4

30

02 Ranger Add Mathematics Tg4.indd 30 25/02/2022 9:10 AM