Persamaan grafik fungsi kuadrat berikut adalah .....

Pertanyaan

$straight y equals negative 1 over 6 straight x squared minus 2 straight x minus 6$
$straight y equals 1 over 6 straight x squared plus 2 straight x plus 6$
$straight y equals 6 straight x squared plus 2 straight x plus 36$
$straight y equals straight x squared plus 2 straight x minus 6$
$straight y equals straight x squared plus 2 straight x plus 6$

Pembahasan Soal:

Gambar grafik fungsi kuadrat dengan puncak P(-6,0) dan melalui titik (0,6).

$left parenthesis negative space 6 comma 0 right parenthesis rightwards arrow straight x subscript straight p equals negative 6$ dan $straight y subscript straight p space equals space 0$

Persamaan fungsi kuadratnya:

$straight y space equals space straight a left parenthesis straight x space minus space straight x subscript straight p right parenthesis squared space plus straight y subscript straight p straight y equals straight a left parenthesis straight x plus 6 right parenthesis squared space plus 0 straight y space equals space straight a left parenthesis straight x space plus space 6 right parenthesis squared space... space left parenthesis straight i right parenthesis$

Karena melalui (0,6), maka:

$straight y equals straight a left parenthesis straight x plus 6 right parenthesis squared 6 space equals space straight a left parenthesis 0 space plus space 6 right parenthesis squared space 6 space equals space 36 straight a straight a equals 6 over 36 equals 1 over 6$

Substitusikan $a equals 1 over 6$ ke persamaan (i) sehingga diperoleh:

$straight y equals 1 over 6 left parenthesis straight x plus 6 right parenthesis squared straight y equals 1 over 6 left parenthesis straight x squared plus 12 straight x plus 36 right parenthesis straight y equals 1 over 6 straight x squared plus 2 straight x plus 6 right parenthesis$

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 22 Desember 2020

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