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] 28 SE Production Limited