Revision
Curve Sketching
Question 1:
The figure below shows the graph of y  ( x  3)( x  7) .
Find
y
a) the values of m and n.
b) the equation of the line of symmetry.
c) the coordinates of the minimum point.
y  ( x  3)( x  7)
x
0
m
n
Revision
Curve Sketching
Question 2:
The curve y  ( x  3)( x  8) cuts the x-axis at the points A and B,
y
and the y-axis at point C.
a) Write down the coordinates of the points A, B and C.
b) Find the equation of the line of symmetry of the curve.
A
O
y  ( x  3)( x  8) C
x
B
Revision
Curve Sketching
Question 3:
The curve y  6  3x  3x cuts the y-axis at A
as shown in the diagram.
a) Find the coordinates of A.
b) Write down the equation of the line of symmetry.
c) Given that the point B(5, k) lies on the curve,
find the value of k.
2
Revision
Curve Sketching
Question 4:
The curve y  x  6x  2 cuts the x-axis at P and Q
as shown in the figure below.
a) Write down the coordinates of P and Q.
b) State the equation of the line of symmetry of the curve.
P
y
O
Q
x
Revision
Curve Sketching
Question 5:
Sketch the graph of
y  ( x  3)( x  2) .
Revision
Curve Sketching
Question 6:
a) Sketch the graph of y  ( x  2)( x  3) .
b) Write down the equation of the line of symmetry of y  ( x  2)( x  3) .
Revision
Curve Sketching
Question 7:
Sketch the graph of y  (3  x)( x  2) .
Revision
Curve Sketching
Question 8:
Sketch the graph of y  (3  x)(5  x) .
Revision
Curve Sketching
Question 9:
2
2
a) Express x  4 x  5 in the form ( x  a)  b .
b) Sketch the graph of
y  x 2  4x  5 .
Revision
Curve Sketching
Question 10:
2
2
a) Express x  2 x  4 in the form ( x  p )  q .
2
b) Sketch the graph of y  x  2 x  4 .
Revision
Curve Sketching
Question 11:
2
a) Express x  2 x  2 in the form ( x  a)2  b .
b) Sketch the graph of y  x  2 x  2 .
2
c) Write down the coordinates of the turning point of y  x 2  2 x  2 .
Revision
Curve Sketching
Question 12:
a) Express y  x 2  4 x  5 in the form ( x  a) 2  b .
b) Sketch the graph of y  x 2  4 x  5 on the axes in the answer space, indicating
clearly the turning point and the y-intercept.
Revision
Curve Sketching
Question 13:
a) Sketch the graph of y = -(x - 3)2 + 2 .
b) Write down the equation of the line of symmetry of the graph.
c) Find the coordinates of the minimum or maximum point.
Revision
Curve Sketching
Question 14:
2
a) Sketch the graph of y  4  ( x  1)
(GCE O Levels E Math, Nov 2010 Paper 1 Q19a)
b) Find the coordinates of the maximum point.
Revision
Curve Sketching
Question 15:
Sketch the graph of
y  3  ( x  2) 2 .
Revision
Curve Sketching
Question 16:
2
a) Sketch the graph of y  ( x  3)  9 , showing clearly the coordinates of the
turning point and all intercepts.
b) Write down the equation of the line of symmetry of y  ( x  3)  9 .
2
Revision
Curve Sketching
Revision Accomplished!