Analysis and Approaches for IBDP Maths Ebook 1 | Page 37

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(d) f ( x) � g( x)
2 2
( x 3) 1 ( x 5) 19
� � � � � � M1
2 2
x x x x
2 2
� 6 �9�1� � �10 � 25 � 19
(A1) for expansion
x � 6x �8 � �x �10x
� 6
(A1) for simplification
2
2x
�16x�14 � 0
A1
2
x �8x� 7 � 0
( x� 7)( x�1) � 0
(A1) for factorization
x �� 7 or x �� 1
A2 N3
[7]
3
Exercise 10
1. A quadratic function f is given by
2
f ( x) ( x h)
k
� � � � .
The vertex of the graph of f is at (3, � 1) , and the graph crosses the y -axis at the point
(0, c ) .
(a) Write down the value of h and of k .
[2]
(b) Find the value of c.
[2]
2
Let g( x) � ( x �1) � 5 . The graph of g is obtained by a reflection of the graph of f in
� p �
the x -axis, followed by a translation of � �.
�q
�
(c) Find the value of p and of q .
[5]
(d) Find the y -coordinates of the points of intersection of the graphs of f and g .
[5]
2. A quadratic function f is given by
2
f ( x) ( x h)
k
� � � .
The vertex of the graph of f is at (1, � 6) , and the graph crosses the y -axis at the point
(0, c ) .
(a) Write down the value of h and of k .
[2]
(b) Find the value of c.
[2]
2
Let g( x) � ( x �3) � 18 . The graph of g is obtained by a reflection of the graph of f in
� p �
the y -axis, followed by a translation of � �.
�q
�
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