Roboguru

Perhatikan persamaan kuadrat berikut Pada persamaan fungsi kuadrat diatas yang mempunyai nilai minimum adalah ...

Pertanyaan

Perhatikan persamaan kuadrat berikut

table row straight i cell f open parentheses x close parentheses equals x squared plus 3 x plus 4 end cell row ii cell f open parentheses x close parentheses equals negative 2 x squared plus 4 x plus 5 end cell row iii cell f open parentheses x close parentheses equals x squared minus 1 end cell row iv cell f open parentheses x close parentheses equals 6 plus 5 x minus 2 x squared end cell end table

Pada persamaan fungsi kuadrat diatas yang mempunyai nilai minimum adalah ...

Pembahasan Soal:

Uji masing-masing persamaan kuadrat yang disajikan.

  • f open parentheses x close parentheses equals x squared plus 3 x plus 4

a equals 1b equals 3 dan c equals 4.

Nilai minimum fungsi:

table attributes columnalign right center left columnspacing 0px end attributes row cell f subscript m i n end subscript end cell equals cell fraction numerator negative open parentheses b squared minus 4 a c close parentheses over denominator 4 a end fraction end cell row blank equals cell fraction numerator negative open parentheses 3 squared minus 4 open parentheses 1 close parentheses open parentheses 4 close parentheses close parentheses over denominator 4 open parentheses 1 close parentheses end fraction end cell row blank equals cell fraction numerator negative open parentheses 9 minus 16 close parentheses over denominator 4 end fraction end cell row blank equals cell fraction numerator negative open parentheses negative 7 close parentheses over denominator 4 end fraction end cell row blank equals cell 7 over 4 end cell row blank equals cell 1 comma 75 end cell end table

 

  • f open parentheses x close parentheses equals negative 2 x squared plus 4 x plus 5

a equals negative 2b equals 4 dan c equals 5.

Nilai minimum fungsi:

table attributes columnalign right center left columnspacing 0px end attributes row cell f subscript m i n end subscript end cell equals cell fraction numerator negative open parentheses b squared minus 4 a c close parentheses over denominator 4 a end fraction end cell row blank equals cell fraction numerator negative open parentheses 4 squared minus 4 open parentheses negative 2 close parentheses open parentheses 5 close parentheses close parentheses over denominator 4 open parentheses negative 2 close parentheses end fraction end cell row blank equals cell fraction numerator negative open parentheses 16 minus open parentheses negative 40 close parentheses close parentheses over denominator negative 8 end fraction end cell row blank equals cell fraction numerator negative open parentheses 16 plus 40 close parentheses over denominator negative 8 end fraction end cell row blank equals cell fraction numerator negative 56 over denominator negative 8 end fraction end cell row blank equals 7 end table

 

  • f open parentheses x close parentheses equals x squared minus 1

a equals 1b equals 0 dan c equals negative 1.

Nilai minimum fungsi:

table attributes columnalign right center left columnspacing 0px end attributes row cell f subscript m i n end subscript end cell equals cell fraction numerator negative open parentheses b squared minus 4 a c close parentheses over denominator 4 a end fraction end cell row blank equals cell fraction numerator negative open parentheses 0 squared minus 4 open parentheses 1 close parentheses open parentheses negative 1 close parentheses close parentheses over denominator 4 open parentheses 1 close parentheses end fraction end cell row blank equals cell fraction numerator negative open parentheses 0 minus open parentheses negative 4 close parentheses close parentheses over denominator 4 end fraction end cell row blank equals cell fraction numerator negative open parentheses 0 plus 4 close parentheses over denominator 4 end fraction end cell row blank equals cell fraction numerator negative 4 over denominator 4 end fraction end cell row blank equals cell negative 1 end cell end table

 

  • f open parentheses x close parentheses equals 6 plus 5 x minus 2 x squared

a equals negative 2b equals 5 dan c equals 6.

Nilai minimum fungsi:

table attributes columnalign right center left columnspacing 0px end attributes row cell f subscript m i n end subscript end cell equals cell fraction numerator negative open parentheses b squared minus 4 a c close parentheses over denominator 4 a end fraction end cell row blank equals cell fraction numerator negative open parentheses 5 squared minus 4 open parentheses negative 2 close parentheses open parentheses 6 close parentheses close parentheses over denominator 4 open parentheses negative 2 close parentheses end fraction end cell row blank equals cell fraction numerator negative open parentheses 25 minus open parentheses negative 48 close parentheses close parentheses over denominator negative 8 end fraction end cell row blank equals cell fraction numerator negative open parentheses 25 plus 48 close parentheses over denominator negative 8 end fraction end cell row blank equals cell fraction numerator negative 73 over denominator negative 8 end fraction end cell row blank equals cell 9 comma 125 end cell end table

Maka, persamaan fungsi kuadrat diatas yang mempunyai nilai minimum adalah f open parentheses x close parentheses equals x squared minus 1.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Mei 2021

Ruangguru

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved