[tex]\displaystyle\rm~f(x) = {x}^{2} - x - 6[/tex]
Penjelasan dengan langkah-langkah:
Berdasarkan grafik, fungsi kuadrat memotong sumbu-x di titik (-2,0) dan (3,0) serta melalui titik (0,-6).
Maka :
[tex]\displaystyle\rm~x_1 = -2~dan~x_2 = 3[/tex]
Penyelesaian :
[tex]\colorbox{thistle}{\color{purple}{\boxed{\displaystyle\bf~{y = a(x - x_1)(x - x_2)}}}}[/tex]
[tex]\displaystyle\rm~y = a(x - x_1)(x - x_2) \\ \displaystyle\rm~ - 6 = (0 + 2)(0 - 3) \\ \displaystyle\rm~ - 6 = a( 2)( - 3) \\ \displaystyle\rm~ - 6 = a( - 6) \\ \displaystyle\rm~ - 6 = - 6a \\ \displaystyle\rm~a = 1[/tex]
[tex]\displaystyle\rm~y = a(x - x_1)(x - x_2) \\ \displaystyle\rm~y = 1(x + 2)(x - 3) \\ \displaystyle\rm~y = (x + 2)(x - 3) \\ \displaystyle\rm~y = {x}^{2} - 3x + 2x - 6 \\ \displaystyle\rm~y = {x}^{2} - x - 6[/tex]
Jadi, jawabannya c.
