Jika fungsi untuk grafik di bawah ini adalah y=ax2+bx+c, maka nilai a+b−c adalah ...

Pertanyaan

Jika fungsi untuk grafik di bawah ini adalah y equals straight a x squared plus straight b x plus straight c, maka nilai a and b bond c adalah ...

  1. negative 12

  2. 10

  3. 12

  4. 14

  5. 18

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Diketahui:

Grafik fungsi kuadrat.

Titik potong grafik tehadap sumbu x adalah open parentheses 1 comma space 0 close parentheses dan open parentheses 3 comma space 0 close parentheses.

Titik puncak grafik fungsi kuadrat open parentheses 2 comma space 2 close parentheses.

Bentuk umum fungsi kuadrat adalah y equals straight a x squared plus straight b x plus straight c.

Kemudian substitusi titik-titik yang diketahui ke bentuk umum fungsi kuadrat:

  • Tititk open parentheses 1 comma space 0 close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell straight a x squared plus straight b x plus straight c end cell row 0 equals cell straight a open parentheses 1 close parentheses squared plus straight b open parentheses 1 close parentheses plus straight c end cell row 0 equals cell straight a plus straight b plus straight c space space space space space space space space space space space space... left parenthesis 1 right parenthesis end cell end table

  • Titik open parentheses 3 comma space 0 close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell straight a x squared plus straight b x plus straight c end cell row 0 equals cell straight a open parentheses 3 close parentheses squared plus straight b open parentheses 3 close parentheses plus straight c end cell row 0 equals cell 9 straight a plus 3 straight b plus straight c space space space space space space space space... left parenthesis 2 right parenthesis end cell end table

  • Titik open parentheses 2 comma space 2 close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell straight a x squared plus straight b x plus straight c end cell row 2 equals cell straight a open parentheses 2 close parentheses squared plus straight b open parentheses 2 close parentheses plus straight c end cell row 2 equals cell 4 straight a plus 2 straight b plus straight c space space space space space space space space... left parenthesis 3 right parenthesis end cell end table

Tentukan nilai a, b, dan c dengan metode eliminasi dan substitusi.

Eliminasi persamaan open parentheses 1 close parentheses dan open parentheses 2 close parentheses.

table attributes columnalign right center left end attributes row cell straight a plus straight b plus straight c end cell equals 0 row cell 9 straight a plus 3 straight b plus straight c end cell equals cell 0 space space minus end cell row cell negative 8 straight a minus 2 straight b space space space end cell equals cell 0 space space space... left parenthesis 4 right parenthesis end cell end table

Eliminasi persamaan open parentheses 2 close parentheses dan open parentheses 3 close parentheses.

table attributes columnalign right center left end attributes row cell 9 straight a plus 3 straight b plus straight c end cell equals 0 row cell 4 straight a plus 2 straight b plus straight c end cell equals cell 2 space space space space minus end cell row cell 5 straight a plus straight b space space space space space space space end cell equals cell negative 2 space space space... left parenthesis 5 right parenthesis end cell end table

Eliminasi persamaan open parentheses 4 close parentheses dan open parentheses 5 close parentheses.

table attributes columnalign center center center center center center left end attributes row cell negative 8 straight a minus 2 straight b end cell equals 0 cell open vertical bar cross times 1 close vertical bar end cell cell negative 8 straight a minus 2 straight b end cell equals 0 row cell 5 straight a plus straight b end cell equals cell negative 2 end cell cell open vertical bar cross times 2 close vertical bar end cell cell 10 straight a plus 2 straight b end cell equals cell negative 4 space plus end cell row space space space space cell 2 straight a space space space space space space end cell equals cell negative 4 end cell row space space space space cell straight a space space space space end cell equals cell fraction numerator negative 4 over denominator 2 end fraction end cell row space space space space cell straight a space space space space end cell equals cell negative 2 end cell end table

Substitusi nilai a ke persamaan open parentheses 4 close parentheses.

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 8 straight a minus 2 straight b end cell equals 0 row cell negative 8 open parentheses negative 2 close parentheses minus 2 straight b end cell equals 0 row cell 16 minus 2 straight b end cell equals 0 row cell negative 2 straight b end cell equals cell negative 16 end cell row straight b equals cell fraction numerator negative 16 over denominator negative 2 end fraction end cell row straight b equals 8 end table

Substitusi nilai a dan b ke persamaan open parentheses 1 close parentheses.

table attributes columnalign right center left columnspacing 0px end attributes row cell straight a plus straight b plus straight c end cell equals 0 row cell negative 2 plus 8 plus straight c end cell equals 0 row cell 6 plus straight c end cell equals 0 row straight c equals cell negative 6 end cell end table

Diperoleh a equals minus sign 2b equals 8, dan c equals minus sign 6.

Maka, nilai dari a and b bond c adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell a and b bond c end cell equals cell negative sign 2 plus 8 minus sign open parentheses negative sign 6 close parentheses end cell row blank equals cell 6 plus 6 end cell row blank equals 12 end table

Maka nilai a and b bond c adalah 12.

Jadi, jawaban yang tepat adalah C.

55

2.5 (2 rating)

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