Analysis and Approaches for IBDP Maths Ebook 1 | Page 20

Your Practice Set – Analysis and Approaches for IBDP Mathematics 5 Paper 1 Section B – Find the unknown coefficients of a tangent Example A quadratic function f can be written in the form f ( x) � a( x � p)( x � 7) . The graph of f has axis of symmetry x � 3 and y -intercept at (0, � 7) . (a) Find the value of p . (b) Find the value of a . (c) The line y �mx � 11 is a tangent to the curve of f . Find the values of m . [3] [3] [8] Solution (a) x � 7 is one of the x -intercepts. (M1) for valid approach p � 7 3 2 (M1) for correct formula p �� 1 A1 N2 [3] (b) �7 � a(0 �( �1))(0 � 7) (M1) for substitution �7� � 7a (A1) for simplification a � 1 A1 N2 [3] (c) A tangent only intersects with a curve once. (M1) for correct property It implies that the corresponding discriminant equals to 0. R1 ( x �( �1))( x �7) � mx � 11 (M1) for setting equation 2 x x mx 2 x �6 �7 � � 11 � ( �6 � m) x � 4 � 0 (M1) for quadratic equation 2 ( 6 m) 4(1)(4) 0 � � � � A1 2 36 �12m� m �16 � 0 2 m �12m� 20 � 0 ( m� 2)( m�10) � 0 (A1) for factorization m �� 2 or m �� 10 A2 N0 [8] 12 SE Production Limited