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Pertanyaan

Kurva y equals negative x squared plus 8 x minus 6 terletak di atas kurva y equals x squared minus 8 x plus 18 untuk ....

  1. negative 18 less than x less than 6 

  2. negative 6 less than x less than 8 

  3. negative 4 less than x less than 4 

  4. 2 less than x less than 6 

  5. 6 less than x less than 18 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Pada soal diketahui kurva y equals negative x squared plus 8 x minus 6 terletak di atas kurva y equals x squared minus 8 x plus 18, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell negative x squared plus 8 x minus 6 end cell greater than cell x squared minus 8 x plus 18 end cell row cell negative x squared plus 8 x minus 6 plus 6 end cell greater than cell x squared minus 8 x plus 18 plus 6 end cell row cell negative x squared plus 8 x end cell greater than cell x squared minus 8 x plus 24 end cell row cell negative x squared minus x squared plus 8 x plus 8 x end cell greater than 24 row cell negative 2 x squared plus 16 x end cell greater than 24 row cell fraction numerator negative 2 x squared over denominator negative 2 end fraction plus fraction numerator 16 x over denominator negative 2 end fraction end cell less than cell fraction numerator 24 over denominator negative 2 end fraction end cell row cell x squared minus 8 x end cell less than cell negative 12 end cell row cell x squared minus 8 x plus 12 end cell less than 0 row cell open parentheses x minus 2 close parentheses open parentheses x minus 6 close parentheses end cell less than 0 end table

Buat pertidaksamaan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x minus 2 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x minus 6 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank less than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table menjadi persamaan kuadrat sehingga diperoleh solusi untuk x.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x minus 2 close parentheses open parentheses x minus 6 close parentheses equals 0 x minus 2 equals 0 rightwards double arrow x subscript 1 equals 2 x minus 6 equals 0 rightwards double arrow x subscript 2 equals 6 end cell end table

Selanjutnya, gunakan garis bilangan dan lakukan uji titik untuk memperoleh penyelesaiaan pertidaksamaan dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x minus 2 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x minus 6 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank less than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table sebagai berikut:

Dengan demikian, Kurva y equals negative x squared plus 8 x minus 6 terletak di atas kurva y equals x squared minus 8 x plus 18 pada 2 less than x less than 6.

Oleh karena itu, jawaban yang benar adalah D.

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