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Diketahui ordinat titik puncak fungsi kuadrat  ada...

Diketahui ordinat titik puncak fungsi kuadrat begin mathsize 14px style f open parentheses x close parentheses equals a x squared plus b x plus c end style adalah 2. Jika begin mathsize 14px style f open parentheses 2 close parentheses equals f open parentheses 4 close parentheses equals 0 end style maka begin mathsize 14px style a plus b plus c end style adalah ....

Jawaban:

Diketahui ordinat titik puncak fungsi kuadrat begin mathsize 14px style f open parentheses x close parentheses equals a x squared plus b x plus c end style adalah 2. Jika begin mathsize 14px style f open parentheses 2 close parentheses equals f open parentheses 4 close parentheses equals 0 end style, maka:

- Tentukan nilai begin mathsize 14px style f open parentheses 2 close parentheses equals 0 end style 

begin mathsize 14px style space space space space space space space space space space space f open parentheses x close parentheses equals a x squared plus b x plus c space space space space space space space space space space space f open parentheses 2 close parentheses equals a open parentheses 2 close parentheses squared plus b open parentheses 2 close parentheses plus c space space space space space space space space space space space space space space space 0 equals a open parentheses 4 close parentheses plus 2 b plus c space space space space space space space space space space space space space space space 0 equals 4 a plus 2 b plus c 4 a plus 2 b plus c equals 0 space... space left parenthesis 1 right parenthesis end style 

- Tentukan nilai begin mathsize 14px style f open parentheses 4 close parentheses equals 0 end style 

begin mathsize 14px style space space space space space space space space space space space space space space f left parenthesis x right parenthesis equals a x squared plus b x plus c space space space space space space space space space space space space space space f left parenthesis 4 right parenthesis equals a left parenthesis 4 right parenthesis squared plus b left parenthesis 4 right parenthesis plus c space space space space space space space space space space space space space space space space space space 0 equals a left parenthesis 16 right parenthesis plus 4 b plus c space space space space space space space space space space space space space space space space space space 0 equals 16 a plus 4 b plus c 16 a plus 4 b plus c equals 0 space... space left parenthesis 2 right parenthesis end style 

- Eliminasi (1) dan (2)

begin mathsize 14px style stack attributes charalign center stackalign right end attributes row 4 a plus 2 b plus c equals 0 end row row 16 a plus 4 b plus c equals 0 end row horizontal line row minus 12 a minus 2 b equals 0 end row row 12 a plus 2 b equals 0 end row end stack space minus end style 

- Menentukan nilai undefined 

begin mathsize 14px style 12 a plus 2 b equals 0 2 open parentheses 6 a plus b close parentheses equals 0 space space space space 6 a plus b equals 0 space space space space space space space space space space space space b equals negative 6 a end style 

- Substitusi nilai begin mathsize 14px style b end style ke (1)

begin mathsize 14px style space space space space space space space 4 a plus 2 b plus c equals 0 4 a plus 2 open parentheses negative 6 a close parentheses plus c equals 0 space space space space space 4 a minus 12 a plus c equals 0 space space space space space space space space space space space minus 8 a plus c equals 0 space space space space space space space space space space space space space space space space space space space space space c equals 8 a end style 

- Menentukan nilai undefined 

begin mathsize 14px style space space space space space space space space f open parentheses x close parentheses equals a x squared plus b x plus c space space space space space space space space f open parentheses x close parentheses equals a x squared plus open parentheses negative 6 a close parentheses x plus open parentheses 8 a close parentheses space space space space space space space space f open parentheses x close parentheses equals a x squared minus 6 a x plus 8 a space space space space space space space f apostrophe open parentheses x close parentheses equals 2 a x minus 6 a space space space space space space space space space space space space 0 equals 2 a x minus 6 a 2 a x minus 6 a equals 0 space space space space space space space space 2 a x equals 6 a space space space space space space space space space space space space x equals fraction numerator 6 a over denominator 2 a end fraction space space space space space space space space space space space space x equals 3 end style 

- Karena ordinat titik puncak fungsi adalah begin mathsize 14px style 2 end style, maka:

begin mathsize 14px style space space space space space space space space space space space space space space space space space space space space space space f open parentheses 3 close parentheses equals 2 a open parentheses 3 close parentheses squared minus 6 a open parentheses 3 close parentheses plus 8 a equals 2 space space space space a open parentheses 9 close parentheses minus 18 a plus 8 a equals 2 space space space space space space space 9 a minus 18 a plus 8 a equals 2 space space space space space space space space space space space space space space space space space space space space space space minus a equals 2 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 negative 2 end style 

- Substitusi nilai begin mathsize 14px style a space ke space b end style 

begin mathsize 14px style b equals negative 6 a b equals negative 6 open parentheses negative 2 close parentheses b equals 12 end style 

- Substitusi nilai begin mathsize 14px style straight a space ke space straight c end style 

begin mathsize 14px style c equals 8 a c equals 8 open parentheses negative 2 close parentheses c equals negative 16 end style 

- Hitung nilai undefined dengan cara:

begin mathsize 14px style a plus b plus c equals open parentheses negative 2 close parentheses plus 12 plus open parentheses negative 16 close parentheses a plus b plus c equals negative 2 plus 12 minus 16 a plus b plus c equals negative 6 end style 

Jadi, hasil dari undefined adalah begin mathsize 14px style negative 6 end style.

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