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]
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