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Paper 1 – Transformations of Quadratic Functions
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Example
A quadratic function f is given by f x
2
( ) ( x 3 ) 1 � � � .
Let gx ( ) be another quadratic function . The graph of g is obtained by a reflection of the graph of f in the x -axis .
( a ) Find gx ( ), giving the answer in the form
Let h x
2
( ) ( x 5 ) 19
2 a( x m) n � � .
� � � � . The graph of h is obtained from g by a translation of
[ 2 ]
� p � � �.
�q �
( b ) Find the values of
( i ) p ;
( ii ) q . [ 4 ]
Solution
( a ) g( x) �� f ( x)
( M1 ) for valid approach g x
2
( ) � �(( x �3 ) � 1 ) g x
2
( ) ( x 3 ) 1 � � � � A1
( b ) ( i ) �3� p � � 5 ( M1 ) for translation p �� 2
( ii ) 1�q
� 19
( M1 ) for translation
A1 q � 18 A1
[ 2 ]
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