計一條有關function的數 10分

ai ) As GH = 4, so GM = 1 and MH = 3.

Therefore g = -1 and h = 3.



ii) x – coordinate of T = ( - 1 + 3 ) / 2 = 1

y – coordinate of T = - 3k

So T ( 1 , - 3k )



bi) The vertex of P1 which is T has been transferred to H in P2.

So, referring to E ( x ) = D ( x +α) + 8 and H ( 3, k )

1 - α = 3

α= -2

-3k + 8 = k

4k = 8

k = 2

As F ( x ) = βx2 + 16 x + 16 passes through G ( - 1 , 2 ), so

β( - 1 )2 + 16 ( - 1 ) + 16 = 2

β = 2



ii) D ( x ) = ( x – 1 )2 – 3 ( 2 )

= ( x – 1 )2 – 6



E ( x ) = ( x - 2 – 1 )2 – 3 ( 2 ) + 8

= ( x - 3 )2 + 2



F ( x ) = 2 x2 + 16 x + 16

= 2 ( x + 4 )2 – 16



iii) F ( x ) is obtained by narrowing E ( x ) then move 7 units to the left and 18 units downwards.



iv) D ( x ) = ( x – 1 )2 – 6

= x2 – 2x + 1 – 6

= x2 – 2x – 5

So a = 1, b = -2 and c = -5