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Suatu grafik fungsi kuadrat  melalui tiga titik yaitu , , dan . Rumus fungsi tersebut adalah ....

Pertanyaan

Suatu grafik fungsi kuadrat begin mathsize 14px style f open parentheses x close parentheses end style melalui tiga titik yaitu begin mathsize 14px style open parentheses 1 comma space 8 close parentheses end stylebegin mathsize 14px style open parentheses 2 comma space 0 close parentheses end style, dan begin mathsize 14px style open parentheses 5 comma space 0 close parentheses end style. Rumus fungsi tersebut adalah .... 

  1. ...space 

  2. ...undefined 

Pembahasan Video:

Pembahasan Soal:

Bentuk umum persamaan kuadrat yang digunakan adalah begin mathsize 14px style y equals a x squared plus b x plus c end style.

Substitusi tiga titik pada bentuk umum persamaan kuadrat:

  • Persamaan (1): untuk titik begin mathsize 14px style open parentheses 1 comma space 8 close parentheses end style 

begin mathsize 14px style f open parentheses x close parentheses equals a x squared plus b x plus c space space space space 8 equals a open parentheses 1 close parentheses squared plus b open parentheses 1 close parentheses plus c space space space space space 8 equals a plus b plus c space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis end style

  • Persamaan (2): untuk titik begin mathsize 14px style open parentheses 2 comma space 0 close parentheses end style

begin mathsize 14px style f open parentheses x close parentheses equals a x squared plus b x plus c space space space space 0 equals a open parentheses 2 close parentheses squared plus b open parentheses 2 close parentheses plus c space space space space 0 equals 4 a plus 2 b plus c space space space space space space space space... left parenthesis 2 right parenthesis end style

  • Persamaan (2): untuk titik begin mathsize 14px style open parentheses 5 comma space 0 close parentheses end style

begin mathsize 14px style f open parentheses x close parentheses equals a x squared plus b x plus c space space space space 0 equals a open parentheses 5 close parentheses squared plus b open parentheses 5 close parentheses plus c space space space space 0 equals 25 a plus 5 b plus c space space space space space space space space space... left parenthesis 3 right parenthesis end style

Berikutnya adalah mencari nilai a, b, dan c dengan metode eliminasi dan subsitusi.

Eliminasi variabel begin mathsize 14px style c end style dari persamaan (1) dan (2) seperti berikut:

begin mathsize 14px style space space space space a plus b plus down diagonal strike c equals 8 bottom enclose 4 a plus 2 b plus down diagonal strike c equals 0 space space minus end enclose space space space space minus 3 a minus b equals 8 space space space space space space space space... left parenthesis 4 right parenthesis end style  

Eliminasi variabel begin mathsize 14px style c end style dari persamaan (2) dan (3) seperti berikut:

begin mathsize 14px style space space 4 a plus 2 b plus down diagonal strike c equals 0 bottom enclose 25 a plus 5 b plus down diagonal strike c equals 0 space space minus end enclose space space minus 21 a minus 3 b equals 0 space space space space space space space space space... left parenthesis 5 right parenthesis end style 

Kemudian gunakan metode eliminasi untuk mengetahui nilai a dan b seperti berikut:

begin mathsize 14px style space space space space minus 3 a minus b equals 8 space space space space open vertical bar cross times 3 close vertical bar space space space space space minus 9 a minus 3 b equals 24 minus 21 a minus 3 b equals 0 space space space space space bottom enclose open vertical bar cross times 1 close vertical bar space space minus 21 a minus 3 b equals 0 space space minus end enclose space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 12 a equals 24 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space a equals 24 over 12 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space a equals 2 end style

Kemudian substitusi begin mathsize 14px style a equals 2 end style ke persamaan begin mathsize 14px style open parentheses 4 close parentheses end style seperti berikut:

begin mathsize 14px style space space minus 21 a minus 3 b equals 0 minus 21 open parentheses 2 close parentheses minus 3 b equals 0 space space space space space minus 42 minus 3 b equals 0 space space space space space space space space space space space space space minus 42 equals 3 b space space space space space space space space space space space space fraction numerator negative 42 over denominator 3 end fraction equals b space space space space space space space space space space space space space minus 14 equals b end style

Kemudian substitusi begin mathsize 14px style a equals 2 end style dan begin mathsize 14px style b equals negative 14 end style ke persamaan begin mathsize 14px style open parentheses 1 close parentheses end style seperti berikut:

begin mathsize 14px style space space space space space space space a plus b plus c equals 8 2 plus open parentheses negative 14 close parentheses plus c equals 8 space space space space space space 2 minus 14 plus c equals 8 space space space space space space space space minus 12 plus c equals 8 space space space space space space space space space space space space space space space space space space space space c equals 8 plus 12 space space space space space space space space space space space space space space space space space space space space c equals 20 end style

Sehingga didapat begin mathsize 14px style a equals 2 end stylebegin mathsize 14px style b equals negative 14 end style, dan begin mathsize 14px style c equals 20 end style.

Persamaan kuadrat yang terbentuk adalah:

begin mathsize 14px style y equals a x squared plus b x plus c y equals 2 x squared plus open parentheses negative 14 close parentheses x plus 20 y equals 2 x squared minus 14 x plus 20 end style 

 

 

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Terakhir diupdate 04 Mei 2021

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