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Grafik fungsi mempunyai nilai minimum -15. Persama...

Grafik fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals left parenthesis p plus 2 right parenthesis x squared plus left parenthesis p minus 3 right parenthesis x minus 20 end style mempunyai nilai minimum -15. Persamaan sumbu simetri grafik tersebut adalah...

Jawaban:

Diketahui Grafik fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals left parenthesis p plus 2 right parenthesis x squared plus left parenthesis p minus 3 right parenthesis x minus 20 end style, dengan

begin mathsize 14px style a equals p plus 2 b equals p minus 3 c equals negative 20 end style

mempunyai nilai minimum -15, dengan rumus Yp, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y subscript p end cell equals cell negative fraction numerator D over denominator 4 a end fraction end cell row cell negative 15 end cell equals cell negative fraction numerator b squared minus 4 a c over denominator 4 a end fraction end cell row 15 equals cell fraction numerator left parenthesis p minus 3 right parenthesis squared minus 4 open parentheses p plus 2 close parentheses open parentheses negative 20 close parentheses over denominator 4 open parentheses p plus 2 close parentheses end fraction end cell row cell 60 left parenthesis p plus 2 right parenthesis end cell equals cell p squared minus 6 p plus 9 plus 80 left parenthesis p plus 2 right parenthesis end cell row cell 60 p plus 120 end cell equals cell p squared plus 74 p plus 169 end cell row cell p squared plus 14 p plus 49 end cell equals 0 row cell open parentheses p plus 7 close parentheses open parentheses p plus 7 close parentheses end cell equals 0 row p equals cell negative 7 end cell end table end style

Persamaan sumbu simetri adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row x equals cell x subscript p end cell row blank equals cell negative fraction numerator b over denominator 2 a end fraction end cell row blank equals cell negative fraction numerator p minus 3 over denominator 2 left parenthesis p plus 2 right parenthesis end fraction end cell row blank equals cell negative fraction numerator negative 7 minus 3 over denominator 2 left parenthesis negative 7 plus 2 right parenthesis end fraction end cell row blank equals cell negative 1 end cell end table end style

Jadi, jawaban yang tepat adalah D.

 

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