Materi : Bentuk dan Persamaan Kuadrat

Soal Nomor 1

f(x) = ax² + bx + c

Titik ( 3,0 ) : 9a + 3b + c = 0

Titik ( 7,0 ) : 49a + 7b + c = 0

Titik ( 1,36 ) : a + b + c = 36

Eliminasi ( c )

______________________/

Titik ( 3,0 ) dan ( 1,36 )

9a + 3b + c = 0

a + b + c = 36

____________-

8a + 2b = -36

Titik ( 7,0 ) dan ( 1,36 )

48a + 6b = -36

____________/

Eliminasi ( b )

24a + 6b = - 108

48a + 6b = -36

____________-

- 24a = - 72

a = (-72)/(-24)

a = 3

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8a + 2b = -36

8(3) + 2b = -36

2b = - 36 - 24

2b = - 60

b = -30

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a + b + c = -36

3 - 30 + c = -36

c = 30 - 39

c = -9

f(x) = 3x² - 30x - 9

Soal Nomor 2

Titik ( 2,0 ) : [ x¹ = 2 ]

Titik ( 0,2 ) : c = 2

D = 0 [ menyinggung sumbu x ]

[ x¹ = 2 ] [ x² = a ]

( x - 2 )( x - p ) = 0

x² - 2px + 2p = 0

[ c = 2 ]

2p = 2

p = 1

Maka bentuk fungsinya

f(x) x² - 2x + 2

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