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) = x
2 + 4x + 3
[ A 1.1 ]
1.2 g(x) = x
2 − 2x − 3
[ A 1.2 ]
1.3 h(x) = x
2 − 3x + 2
[ A 1.3 ]
1.4 j(x) = x
2 + 2x − 3
[ A 1.4 ]
1.5 f(x) = −x
2 − 5x − 4
[ A 1.5 ]
1.6 j(x) = −x
2 − 3x + 10
[ A 1.6 ]
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 = x
2 + 5x − 2
[ A 2.1 ]
2.2 y = x
2 − 2x − 4
[ A 2.2 ]
2.3 y = 2x
2 − x − 3
[ A 2.3 ]
2.4 y = 3x
2 − 2x − 5
[ A 2.4 ]
2.5 y = −x
2 − x + 4
[ A 2.5 ]
2.6 y = −2x
2 + 3x − 5
[ A 2.6 ]
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 ]
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 ]
The figure shows the graph of
y = x
2 + 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 ]
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 ]
The diagram shows r=the graphs of
f(x) = −x
2 + 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 ]