Carilah interval nilai m agar setiap parabola berikut menyinggung sumbu X . c. h(x)=21​mx2−2mx+23​m+21​

Pertanyaan

Carilah interval nilai m agar setiap parabola berikut menyinggung sumbu X .

c. h open parentheses x close parentheses equals 1 half m x squared minus 2 m x plus 3 over 2 m plus 1 half

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

 interval nilai m agar parabola h left parenthesis x right parenthesis equals 1 half m x squared minus 2 m x plus 3 over 2 m plus 1 half menyinggung sumbu x adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank m end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fourth end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank atau end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank m end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 1 end table 

Pembahasan

Diketahui h left parenthesis x right parenthesis equals 1 half m x squared minus 2 m x plus 3 over 2 m plus 1 half. Agar grafik menyinggung sumbu x, maka nilai D equals 0, sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row D equals 0 row cell b squared minus 4 a c end cell equals 0 row cell left parenthesis negative 2 m right parenthesis squared minus 4 open parentheses fraction numerator 1 over denominator 2 end fraction close parentheses open parentheses fraction numerator 3 over denominator 2 end fraction m plus fraction numerator 1 over denominator 2 end fraction close parentheses end cell equals 0 row cell 4 m squared minus 3 m minus 1 end cell equals 0 row cell left parenthesis 4 m plus 1 right parenthesis left parenthesis m minus 1 right parenthesis end cell equals 0 row m equals cell negative 1 fourth space atau space m equals 1 end cell end table 

Jadi, interval nilai m agar parabola h left parenthesis x right parenthesis equals 1 half m x squared minus 2 m x plus 3 over 2 m plus 1 half menyinggung sumbu x adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank m end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fourth end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank atau end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank m end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 1 end table 

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