Materi : Bentuk dan Fungsi Persamaan Kuadrat

(1) y = x² - ( p + 2 )x + 2p + 4

{ a = 1, b = - p - 2 , c = 2p + 4 }

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(2) y = x² - 4px + 8p

{ a = 1, b = - 4p, c = 8p }

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Kedua Fungsi punya titik minimum yang sama

Secara Sumbu Simetri

(1) Xp = -b/2a = - ( - p - 2 )/2(1) = ( p + 2 )/2

Yp = D/-4a = ( p² - 12p + 20 )/(-4)

Titik Minimum = - 2( p + 2 )/( p² - 12p + 20 )

Titik Minimum = ( - 2p - 4 )/( p² - 12p + 20 )

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(2) Xp = -b/2a = - ( - 4p )/2(1) = 4p/2

Yp = D/-4a = ( 16p² - 32p )/(-4)

Titik Minimum = ( - 8p )/( 16p² - 32p )

Titik Minimum = - 8( p )/( p )( 2p - 4 )

Titik Minimum = - 8/( 2p - 4 )

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( - 2p - 4 )/( p² - 12p + 20 ) = -8/( 2p - 4 )

( - 2p - 4 )( 2p - 4 ) = - 8( p² - 12p + 20 )

-4( p + 2 )( p - 2 ) = -8( p - 2 )( p - 10 )

-4( p + 2 ) = -8( p - 10 )

p + 2 = -2( p - 10 )

p + 2 = - 2p + 20

3p = 18

[ p = 6 ]

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Salah satu titik minimum

Xp = 4p/2 = 2p = 12

Yp = -8/( 2p - 4 ) = -8/( 12 - 4 ) = -8/8 = -1

Titik minimum = ( 12,-1 )

Kesimpulan

Nilai y pada titik minimum tersebut adalah -1.

Semoga bisa membantu