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Nilai minimum fungsi  adalah ...

Nilai minimum fungsi begin mathsize 14px style f open parentheses x close parentheses equals 2 open parentheses x minus 4 close parentheses squared plus 6 end style adalah ... 

  1. begin mathsize 14px style negative 6 end style 

  2. begin mathsize 14px style negative 4 end style 

  3. begin mathsize 14px style 0 end style 

  4. begin mathsize 14px style 4 end style 

  5. begin mathsize 14px style 6 end style 

Jawaban:

begin mathsize 14px style f open parentheses x close parentheses equals 2 open parentheses x minus 4 close parentheses squared plus 6 end style

Jika diubah ke bentuk umum fungi kuadrat maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis end cell size 14px equals cell size 14px 2 size 14px left parenthesis size 14px x size 14px minus size 14px 4 size 14px right parenthesis to the power of size 14px 2 size 14px plus size 14px 6 size 14px space end cell row blank size 14px equals cell size 14px 2 begin mathsize 14px style left parenthesis x squared minus 8 x plus 16 right parenthesis end style size 14px plus size 14px 6 end cell row blank size 14px equals cell size 14px 2 size 14px x to the power of size 14px 2 size 14px minus size 14px 16 size 14px x size 14px plus size 14px 32 size 14px plus size 14px 6 end cell row cell size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis end cell size 14px equals cell size 14px 2 size 14px x to the power of size 14px 2 size 14px minus size 14px 16 size 14px x size 14px plus size 14px 38 end cell end table   

Jadi begin mathsize 14px style straight a equals 2 end style (koefisien begin mathsize 14px style x squared end stylebegin mathsize 14px style straight b equals negative 16 end style (koefisien begin mathsize 14px style x end style) dan begin mathsize 14px style straight c equals 38 end style (konstanta). Dengan menggunakan rumus titik puncak diperoleh 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell minimum space f open parentheses x close parentheses end cell equals cell fraction numerator straight b squared minus 4 ac over denominator negative 4 straight a end fraction end cell row blank equals cell fraction numerator open parentheses negative 16 close parentheses squared minus 4 times 2 times 38 over denominator negative 4 times 2 end fraction end cell row blank equals cell fraction numerator 256 minus 304 over denominator negative 8 end fraction end cell row blank equals cell fraction numerator negative 48 over denominator negative 8 end fraction end cell row blank equals 6 end table end style 

Jadi jawaban yang teapt adalah E. 

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