WISKUNDE
NOG OEFENINGE

MATHEMATICS
MORE EXERCISES

Completing the square.

A.   Skryf onderstaande uitdrukkings in die
vorm (x + p) 2 + q deur die vierkant te
voltooi / die kwadraat te voltooi en skryf
dan die maksimum of minimum waarde
van die uitdrukking neer :

1.  x 2  + 2x + 3                                                [ 1 ]

3.  x2 + 4x ─ 3                                                 [ 3 ]

5.  a2 ─ 3a + 1                                                 [ 5 ]

7.  3p2 ─ 4p ─ 2                                              [ 7 ]

9.  7x2 ─ 2x ─ 5                                               [ 9 ]

11.  − y2 + 5y ─ 6                                            [ 11 ]

13.  − y2 ─ 5y ─ 8                                            [ 13 ]

15.  2a2 ─ 3a + 2                                             [ 15 ]

17.   ─ 3q2 + 2q ─ 8                                        [ 17 ]

B.   Wat moet by elke uitdrukking getel word,
sodat die som 'n volkome vierkant sal
wees?

19.  x2 + 2x                                                      [ 19 ]

21.  a2 + 2a + 4                                               [ 21 ]

23.  q2 ─ 3q ─ 5                                              [ 23 ]

25.  2p2 + p ─ 1                                              [ 25 ]

27.  5x2 ─ 3x + 2                                             [ 27 ]

29.  7y2 + 5y + 4                                              [ 29 ]

A.   Write the following expressions in the
form (x + p) 2 + q by completing the
square and then write down the
maximum or minimum value of
the expression :

2.  x2 − 3x + 2                                               [ 2 ]

4.  x2 ─ 5x + 6                                              [ 4 ]

6.  2a2 ─ 3a + 8                                            [ 6 ]

8.  8q2 + 3q ─ 5                                            [ 8 ]

10.  x2 ─ 2x + 3                                            [ 10 ]

12.  x2 + 3x + 1                                            [ 12 ]

14.  ─ 3a2 ─ 2a ─ 1                                     [ 14 ]

16.  ─ 4p2 + p ─ 1                                       [ 16 ]

18.   ─ 5x2 ─ 3x ─ 7                                   [ 18 ]

B.   What must be added to each
expression so that the sum is
a complete square?

20.  y2 ─ y                                                    [ 20 ]

22.  p2 + 2p ─ 3                                           [ 22 ]

24.  a2 + 2a ─ 5                                           [ 24 ]

26.  3q2 + 2q + 4                                          [ 26 ]

28.  6x2 ─ 5x + 9                                          [ 28 ]

30.  8z2 ─ 3z ─ 7                                          [ 30 ]