Exercise 30
1 . The function f is defined by
2 f ( x) ax bx c
� � � , where a , b , c� . It is given that the graph of f passes through ( 50 , 3600 ) , ( 20 , � 900 ) and ( 5 , � 1125 ) .
( a ) ( i ) Show that 2500a �50b � c � 3600 .
( ii ) Write down the other two equations in a , b and c .
The above three equations can be expressed in a matrix equation
3� 3 matrix , and
�a �
� � X � b and B are two 3� 1 matrices .
�c �
� �
AX �
[ 3 ]
B , where A is a
( b ) Write down
( i ) A ;
7
( ii ) B ;
( iii )
�1
A .
( c ) Hence , find the values of a , b and c .
( d ) Find
[ 4 ]
[ 2 ]
( i ) the x -intercept ( s ) of the graph of f ;
( ii ) the y -coordinate of the vertex . [ 5 ]
2 . The function f is defined by
3 2 f ( x) ax bx cx d
� � � � , where a , b , c , d � . It is given that the graph of f passes through ( 0 , � 384 ), ( 2 , � 840 ), ( 6 , � 2520 ) and ( 10 , � 5544 ).
( a ) ( i ) Show that d �� 384 .
( ii ) Show that 4a � 2b � c � � 228 .
( iii ) Write down the other two equations in a , b and c . [ 4 ] www . seprodstore . com
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