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Diketahui suatu parabola simetris terhadap garis x...

Diketahui suatu parabola simetris terhadap garis x = -2 , dan garis singgung parabola tersebut di titik (0,1) sejajar garis 4x + y = 4 . Titik puncak parabola tersebut adalah ....

  1. (-2, -3)

  2. (-2, -2)

  3. (-2, 0)

  4. (-2, 1)

  5. (-2, 5)

Jawaban:

begin mathsize 14px style Persamaan space parabola colon  straight y equals ax squared plus bx plus straight c    Sumbu space simetri colon  straight x subscript straight p equals negative fraction numerator straight b over denominator 2 straight a end fraction  minus 2 equals negative fraction numerator straight b over denominator 2 straight a end fraction  straight b equals 4 straight a    Parabola space melalui space titik space left parenthesis 0 comma 1 right parenthesis comma space maka colon  straight y equals ax squared plus bx plus straight c  1 equals 0 plus 0 plus straight c  straight c equals 1    Gradien space garis space 4 straight x plus straight y equals 4  straight y equals negative 4 straight x plus 4  straight m subscript 1 equals negative 4  Karena space sejajar comma space maka space straight m subscript 2 equals straight m subscript 1 equals negative 4    straight m equals straight y apostrophe  minus 4 equals 2 ax plus straight b  Substitusikan space straight x equals 0 space left parenthesis karena space melalui space titik space left parenthesis 0 comma 1 right parenthesis right parenthesis  minus 4 equals 0 plus straight b  straight b equals negative 4    straight b equals 4 straight a  minus 4 equals 4 straight a  straight a equals negative 1    Persamaan space parabolanya colon  straight y equals negative straight x squared minus 4 straight x plus 1    Nilai space maksimum colon  straight y subscript straight p equals negative open parentheses negative 2 close parentheses squared minus 4 open parentheses negative 2 close parentheses plus 1  straight y subscript straight p equals negative 4 plus 8 plus 1  straight y subscript straight p equals 5    Maka space titik space puncak colon space left parenthesis negative 2 comma 5 right parenthesis end style

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