Materi : Bentuk dan Persamaan Kuadrat

Soal Nomor 1

y < - 2x² + 8

[ a < 0 ] terbuka ke bawah [ gunung ]

[ D > 0 ] { D = 64 } memotong sumbu x

Titik potong sb x

- 2x² + 8 > 0

2x² < 8

x² < 4

x < ± √4

x < ± 2

Himpunan Penyelesaian

x < 2 atau x < -2 => ( 2,0 ) dan ( -2,0 )

Titik potong sb y

y < - 2(0)² + 8

[ y < 8 ] => ( 0,8 )

Titik Puncak => ( 0,8 )

Xp = -b/2a = -0/2(-2) = 0/4 = 0

Yp = D/-4a = 64/-4(-2) = 64/8 = 8

Soal Nomor 2

y ≥ x² + 2x - 8 [ a > 0 dan D = 36 > 0 ]

Titik potong sb x

x² + 2x - 8 ≤ 0

( x + 4 )( x - 2 ) ≤ 0

Himpunan Penyelesaian

x ≤ -4 atau x ≤ 2 => ( -4,0 ) dan ( 2,0 )

Titik potong sb y

y ≥ 0² + 2(0) - 8

[ y ≥ -8 ] => ( 0,-8 )

Titik Puncak adalah ( -1,-9 )

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

Yp = f(Xp) = (-1)² + 2(-1) - 8 = -9

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5x + 3y + 10 ≥ 0

5x + 3y ≥ -10

Titik potong sb x

5x ≥ -10

[ x ≥ -2 ] => ( -2,0 )

Titik potong sb y

3y ≥ -10

[ y > -10/3 ] => ( 0,-10/3 )

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