Analysis and Approaches for IBDP Maths Ebook 1 | Page 36
Your Practice Set – Analysis and Approaches for IBDP Mathematics
10
Paper 1 Section B – Transformations
in quadratic functions
Example
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 �5) � 19 . 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 x -coordinates of the points of intersection of the graphs of f and g .
[7]
Solution
(a) h �� 3, k �� 1
A2 N2
(b)
(c)
2
f ( x) � ( x �3) � 1
c
� f (0)
(M1) for substitution
2
� (0 � 3) � 1
� 8
A1 N2
2
g( x) � � �
�(( x � p) � 3) �1�
� � q
A1
2
g( x) � �( x � ( �p �3)) � (1 � q)
�p
�3� 5
(M1) for translation
p �� 2
A1 N2
1�q
� 19
(M1) for translation
q � 18
A1 N2
[2]
[2]
[5]
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