Jika puncak grafik fungsi y=px2−qx−1 sama dengan puncak grafik fungsi y=x2−2x+4 maka nilai dari 3p+2q adalah ...

Pertanyaan

Jika puncak grafik fungsi begin mathsize 14px style y equals p x squared minus q x minus 1 end style sama dengan puncak grafik fungsi begin mathsize 14px style y equals x squared minus 2 x plus 4 end style maka nilai dari begin mathsize 14px style 3 p plus 2 q end style adalah ...

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

pertama kita akan menentukan titik puncak fungsi begin mathsize 14px style y equals x squared minus 2 x plus 4 end style

size 14px a size 14px equals size 14px 1 size 14px space size 14px comma size 14px b size 14px equals size 14px minus size 14px 2 size 14px comma size 14px space size 14px d size 14px a size 14px n size 14px space size 14px c size 14px equals size 14px 4 size 14px x subscript size 14px p size 14px equals size 14px minus fraction numerator size 14px b over denominator size 14px 2 size 14px a end fraction size 14px space size 14px space size 14px space size 14px space size 14px equals fraction numerator size 14px minus begin mathsize 14px style left parenthesis negative 2 right parenthesis end style over denominator size 14px 2 size 14px times size 14px 1 end fraction size 14px space size 14px space size 14px space size 14px equals 2 over size 14px 2 size 14px equals size 14px 1 size 14px y subscript size 14px p size 14px equals size 14px f begin mathsize 14px style left parenthesis 1 right parenthesis end style size 14px equals size 14px 1 to the power of size 14px 2 size 14px minus size 14px 2 begin mathsize 14px style left parenthesis 1 right parenthesis end style size 14px plus size 14px 4 size 14px equals size 14px 3 

sehingga titik puncaknya adalah  begin mathsize 14px style open parentheses 1 comma 3 close parentheses end style  

Titik  begin mathsize 14px style open parentheses 1 comma 3 close parentheses end style juga titik puncak dari  begin mathsize 14px style y equals p x squared minus q x minus 1 end style

begin mathsize 14px style x equals negative fraction numerator b over denominator 2 a end fraction 1 equals negative fraction numerator open parentheses negative q close parentheses over denominator 2 p end fraction 1 equals fraction numerator q over denominator 2 p end fraction q equals 2 p space... open parentheses pers space 1 close parentheses y equals p x squared minus q x minus 1 3 equals p open parentheses 1 close parentheses squared minus q open parentheses 1 close parentheses minus 1 3 equals p minus q minus 1 p minus q equals 4 space... open parentheses pers space 2 close parentheses end style 

Subtitusikan pers 1 ke pers 2

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p minus 2 p end cell equals 4 row cell negative p end cell equals 4 row p equals cell negative 4 end cell end table end style 

begin mathsize 14px style p equals minus sign 4 end style disubtitusikan  ke pers 1

begin mathsize 14px style q equals 2 open parentheses negative 4 close parentheses space space equals negative 8 end style 

Nilai begin mathsize 14px style 3 p plus 2 q end style adalah

begin mathsize 14px style 3 open parentheses negative 4 close parentheses plus 2 open parentheses negative 8 close parentheses equals negative 12 plus negative 16 equals negative 28 end style 

 

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