MATHEMATICS
MORE EXERCISES

Question  1
Calculate the intercepts on the axes
and the coordinates of the turning
point and then make a neat sketch
of the parabola :
1.1  f(x) = x2 + 4x + 3                        [ A 1.1 ]
1.2  g(x) = x2 − 2x − 3                        [ A 1.2 ]
1.3  h(x) = x2 − 3x + 2                        [ A 1.3 ]
1.4  j(x) = x2 + 2x − 3                        [ A 1.4 ]
1.5  f(x) = −x2 − 5x − 4                        [ A 1.5 ]
1.6  j(x) = −x2 − 3x + 10                     [ A 1.6 ]

Question  2
Write each of the following in the -
vorm y =a(x + p)2 + q and then
make a neat sketch of the parabola :
2.1  y = x2 + 5x − 2                        [ A 2.1 ]
2.2  y = x2 − 2x − 4                         [ A 2.2 ]
2.3  y = 2x2 − x − 3                         [ A 2.3 ]
2.4  y = 3x2 − 2x − 5                       [ A 2.4 ]
2.5  y = −x2 − x + 4                         [ A 2.5 ]
2.6  y = −2x2 + 3x − 5                     [ A 2.6 ]
Question  3
Determine the equation of each graph :
Points A, B and C are given
3.1
A(−2 ; 0);  B(1 ; 0)   en  C(0 ; −2)            [ A 3.1 ]
3.2
A(2 ; 0);  B(3 ; 0)   en  C(0 ; 6)            [ A 3.2 ]

Question  4
Determine the equation of the parabola
that passes through the following points :

4.1  (−1 ; 0);  (0 ; 3)  and  (2 ; 15)           [ A 4.1 ]
4.2  (−3 ; −12);  (2 ; −7)  and  (5 ; 20)      [ A 4.2 ]
4.3  (−2 ; −15);  (1 ; 0)  and  (4 ; −3)        [ A 4.3 ]
4.4  (−3 ; −14);  (−1 ; 4)  and  (2 ; 1)        [ A 4.4 ]
4.5  The turning point is (2 ; −1);   and a
second point is (4 ; 1)                     [ A 4.5 ]
4.6  The turning point is (1 ; 4);   and a
second point is (−3 ; −12)                [ A 4.6 ]

$$\hspace*{2 mm}\mathrm{4.7\kern3mmThe\ turning\ point\ is\ \Big(−\frac{1}{3} ; \frac{28}{3}\Big)\ and\ a\kern2mm\ }$$
second point is (−4 ; −31)                [ A 4.7 ]

Question  5
The figure shows the graph of
y = x2 + 2x − 8

5.1  Determine the coordinates of
points A, B, C and D.                      [ A 5.1 ]
5.2  Dtermine the lengths of AM,
MD, OM, OC and AC.                      [ A 5.2 ]
5.3  P is the point (−7 ; p).
5.3.1  Determine the value of p.        [ A 5.3.1 ]
5.3.2  Write down the coordinates
of N and Q.                                  [ A 5.3.2 ]
5.3.3  Write down the lengths of
NQ and ND.                                 [ A 5.3.3 ]
5.4  Write down the coordinates of
R and S if RS = 8 units.                 [ A 5.4 ]
5.5  Calculate the length of PW.        [ A 5.5 ]

Question  6
The figure shows the graph of
f(x) = a(x + p)2 + q
D(−1,25 ; −15,125) is the turning point and
P is the point(−6 ; 30)

6.1  Determine the values of
a, p and q.                                       [ A 6.1 ]
6.2  Calculate the coordinates of
points A, B and C.                          [ A 6.2 ]
6.3  Calculate the coordinates of N
if MN = 30 units.                            [ A 6.3 ]
6.4  Determine the coordinates of
point Q.                                           [ A 6.4 ]
6.5  A and Q are points on the graph of
g(x). Determine the equation of
g(x).                                                 [ A 6.5 ]
6.6  Write down the length of ME if
g(x) and the line ND intersect
at E.                                                 [ A 6.6 ]

Question  7
The diagram shows r=the graphs of
f(x) = −x2 + 3x + 10 and g(x) = 10 − 2x

7.1  Calculate the coordinates of
points A, B and C.                         [ A 7.1 ]
7.2  Calculate the coordinates of
D, the turning point.                    [ A 7.2 ]
7.3  Write down the coordinates
of M.                                                [ A 7.3 ]
7.4  Determine the coordinates of P,
the point of intersection of g(x)
with MD.                                        [ A 7.4 ]
7.5  Calculate the lengths of DP
and PM.                                          [ A 7.5 ]
7.6  Q is a point on f(x) and S is a point
on g(x) such that QS ǁ Y-axis.
Determine the
7.6.1  length of QS in terms of x.
[ A 7.6.1 ]
7.6.2  coordinates of Q and S if
QS = 6 units and x > 2.
[ A 7.6.2 ]
7.7  h(x) is formed by transforming f(x)
8 units downwards and
1,5 units to the left. Write down
the equation of h(x).                 [ A 7.7 ]