Parabola ax2+bx+c melalui titik (0, 0), (2, 3), dan (3, 6). Tentukan nilai (a+b+c).

Pertanyaan

Parabola a x squared plus b x plus c melalui titik left parenthesis 0 comma space 0 right parenthesis, left parenthesis 2 comma space 3 right parenthesis, dan left parenthesis 3 comma space 6 right parenthesis. Tentukan nilai left parenthesis a plus b plus c right parenthesis.

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

nilai dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank b end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank c end table adalah 1

Pembahasan

Parabola a x squared plus b x plus c melalui titik left parenthesis 0 comma space 0 right parenthesis, left parenthesis 2 comma space 3 right parenthesis, dan left parenthesis 3 comma space 6 right parenthesis. Maka:

 a left parenthesis 0 right parenthesis squared plus b left parenthesis 0 right parenthesis plus c equals 0 rightwards double arrow c equals 0 space.................. space left parenthesis 1 right parenthesis a left parenthesis 2 right parenthesis squared plus b left parenthesis 2 right parenthesis plus c equals 3 rightwards double arrow 4 a plus 2 b plus c equals 3 space..... space left parenthesis 2 right parenthesis a left parenthesis 3 right parenthesis squared plus b left parenthesis 3 right parenthesis plus c equals 6 rightwards double arrow 9 a plus 3 b plus c equals 6 space...... left parenthesis 3 right parenthesis

Substitusikan c equals 0 ke persamaan (2), maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 a plus 2 b plus 0 end cell equals 3 row cell 4 a plus 2 b end cell equals cell 3 space..... space left parenthesis 4 right parenthesis end cell end table

Substitusikan c equals 0 ke persamaan (3), maka: 

table attributes columnalign right center left columnspacing 0px end attributes row cell 9 a plus 3 b plus 0 end cell equals 6 row cell 9 a plus 3 b end cell equals 6 row cell 3 a plus b end cell equals cell 2 space..... space left parenthesis 5 right parenthesis end cell end table

Eliminasi (4) dan (5), maka:

table row cell 4 a plus 2 b equals 3 end cell cell open vertical bar cross times 1 close vertical bar end cell cell 4 a plus 2 b equals 3 end cell row cell 3 a plus b equals 2 end cell cell open vertical bar cross times 2 close vertical bar end cell cell 6 a plus 2 b equals 4 space minus end cell row blank blank cell negative 2 a equals negative 1 end cell row blank blank cell a equals 1 half end cell end table

Untuk menentukan b, substitusikan nilai a equals 1 half ke salah satu persamaan yaitu table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank b 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 3 end table, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 a plus 2 b end cell equals 3 row cell 4 open parentheses 1 half close parentheses plus 2 b end cell equals 3 row cell 2 plus 2 b end cell equals 3 row cell 2 b end cell equals 1 row b equals cell 1 half end cell end table

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell a plus b plus c end cell equals cell 1 half plus 1 half plus 0 end cell row blank equals 1 end table 

Jadi, nilai dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank b end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank c end table adalah 1

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