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Pertanyaan

Perhatikan gambar berikut.

Sistem pertidaksamaan yang benar untuk daerah yang diarsir pada gambar tersebut adalah ...space 

  1. open curly brackets table attributes columnalign left end attributes row cell y greater or equal than x squared plus 2 x minus 15 end cell row cell y less or equal than negative x squared plus 2 x plus 8 end cell end table close 

  2. open curly brackets table attributes columnalign left end attributes row cell y greater or equal than x squared plus 2 x minus 15 end cell row cell y greater or equal than negative x squared plus 2 x plus 8 end cell end table close 

  3. open curly brackets table attributes columnalign left end attributes row cell y less or equal than x squared plus 2 x plus 15 end cell row cell y less or equal than negative x squared plus 2 x plus 8 end cell end table close 

  4. open curly brackets table attributes columnalign left end attributes row cell y greater or equal than negative x squared plus 2 x plus 8 end cell row cell y less or equal than x squared plus 2 x minus 15 end cell end table close 

  5. open curly brackets table attributes columnalign left end attributes row cell y greater or equal than x squared plus 2 x plus 15 end cell row cell y greater or equal than negative x squared plus 2 x plus 8 end cell end table close 

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.  

Pembahasan

Diketahui parabola pertama melalui titik potong x left parenthesis negative 5 comma space 0 right parenthesisleft parenthesis 3 comma space 0 right parenthesis dan melalui titik left parenthesis 0 comma space minus 15 right parenthesis  

Jika suatu parabola melewati titik potong sumbu x left parenthesis x subscript 1 comma space 0 right parenthesis dan left parenthesis x subscript 2 comma space 0 right parenthesis dan melalui titik left parenthesis x comma space y right parenthesis maka rumus persamaannya yaitu y equals a left parenthesis x minus x subscript 1 right parenthesis left parenthesis x minus x subscript 2 right parenthesis

Misal :

left parenthesis x subscript 1 comma space 0 right parenthesis equals left parenthesis negative 5 comma space 0 right parenthesis left parenthesis x subscript 2 comma space 0 right parenthesis equals left parenthesis 3 comma space 0 right parenthesis left parenthesis x comma space y right parenthesis equals left parenthesis 0 comma space minus 15 right parenthesis 

maka

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell a left parenthesis x minus x subscript 1 right parenthesis left parenthesis x minus x subscript 2 right parenthesis end cell row cell negative 15 end cell equals cell a left parenthesis 0 minus left parenthesis negative 5 right parenthesis right parenthesis left parenthesis 0 minus 3 right parenthesis end cell row cell negative 15 end cell equals cell a left parenthesis 5 right parenthesis left parenthesis negative 3 right parenthesis end cell row cell negative 15 end cell equals cell a left parenthesis negative 15 right parenthesis end cell row a equals 1 end table 

Substitusikan nilai a dan titik potong sumbu x ke y equals a left parenthesis x minus x subscript 1 right parenthesis left parenthesis x minus x subscript 2 right parenthesis

y equals a left parenthesis x minus x subscript 1 right parenthesis left parenthesis x minus x subscript 2 right parenthesis y equals left parenthesis 1 right parenthesis left parenthesis x minus left parenthesis negative 5 right parenthesis right parenthesis left parenthesis x minus 3 right parenthesis y equals left parenthesis x plus 5 right parenthesis left parenthesis x minus 3 right parenthesis y equals x squared plus 2 x minus 15 

Cari letak DHP dengan uji suatu titik dalam DHP

untuk left parenthesis 0 comma space 0 right parenthesis 

y equals x squared plus 2 x minus 15 0 equals 0 squared plus 2 left parenthesis 0 right parenthesis minus 15 0 equals negative 15 

Kita tahu bahwa kurva pembatas dari parabola tersebut adalah garis penuh left parenthesis greater or equal than atau less or equal than right parenthesis dan 0 greater than negative 15 maka pertidakasamaannya yaitu y greater or equal than x squared plus 2 x minus 15 

Selanjutnya diketahui parabola kedua melalui titik potong sumbu x left parenthesis negative 2 comma space 0 right parenthesisleft parenthesis 4 comma space 0 right parenthesis dan melalui titik left parenthesis 0 comma space 8 right parenthesis 

Jika suatu parabola melewati titik potong sumbu x left parenthesis x subscript 1 comma space 0 right parenthesis dan left parenthesis x subscript 2 comma space 0 right parenthesis dan melalui titik left parenthesis x comma space y right parenthesis maka rumus persamaannya yaitu y equals a left parenthesis x minus x subscript 1 right parenthesis left parenthesis x minus x subscript 2 right parenthesis 

Misal :

left parenthesis x subscript 1 comma space 0 right parenthesis equals left parenthesis negative 2 comma space 0 right parenthesis left parenthesis x subscript 2 comma space 0 right parenthesis equals left parenthesis 4 comma space 0 right parenthesis left parenthesis x comma space y right parenthesis equals left parenthesis 0 comma space 8 right parenthesis 

Maka

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell a left parenthesis x minus x subscript 1 right parenthesis left parenthesis x minus x subscript 2 right parenthesis end cell row 8 equals cell a left parenthesis 0 minus left parenthesis negative 2 right parenthesis right parenthesis left parenthesis 0 minus 4 right parenthesis end cell row 8 equals cell a left parenthesis 2 right parenthesis left parenthesis negative 4 right parenthesis end cell row 8 equals cell negative 8 a end cell row a equals cell fraction numerator 8 over denominator negative 8 end fraction end cell row a equals 1 end table 

Substitusikan nilai a dan titik potong sumbu x ke y equals a left parenthesis x minus x subscript 1 right parenthesis left parenthesis x minus x subscript 2 right parenthesis 

y equals a left parenthesis x minus x subscript 1 right parenthesis left parenthesis x minus x subscript 2 right parenthesis y equals left parenthesis negative 1 right parenthesis left parenthesis x minus left parenthesis negative 2 right parenthesis right parenthesis left parenthesis x minus 4 right parenthesis y equals left parenthesis negative 1 right parenthesis left parenthesis x plus 2 right parenthesis left parenthesis x minus 4 right parenthesis y equals left parenthesis negative 1 right parenthesis x squared minus 2 x minus 8 y equals negative x squared plus 2 x plus 8 

Cari letak DHP dengan uji suatu titik dalam DHP 

untuk left parenthesis 0 comma space 0 right parenthesis 

y equals negative x squared plus 2 x plus 8 0 equals negative 0 squared plus 2 left parenthesis 0 right parenthesis plus 8 0 equals 8 

Kita tahu bahwa kurva parabola tersebut merupakan garis penuh left parenthesis greater or equal than atau less or equal than right parenthesis dan 0 less than 8 maka pertidaksamaanya yaitu y less or equal than negative x squared plus 2 x plus 8 

Jadi, sistem pertidaksamaan yang benar adalah open curly brackets table attributes columnalign left end attributes row cell y greater or equal than x squared plus 2 x minus 15 end cell row cell y less or equal than negative x squared plus 2 x plus 8 end cell end table close 

Oleh karena itu, jawaban yang benar adalah A.  

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