For this case we have that by definition, a quadratic function is given by:[tex]f (x) =ax ^ 2+ bx + c[/tex]
We evaluate the given equations:
Option A:
[tex]8-5x =4(3x-1)\\8-5x=12x-4\\8 + 4 = 12x + 5x[/tex]
It is a linear equation!
Option B:
[tex](48 + 271a-1)+1 = 0\\48 + 271a-1+1 = 0\\48 + 271a = 0[/tex]
It is a linear equation!
Option C:
[tex]12y + \frac {2} {3} y-5 = 0\\\frac {36y + 2y} {3} = 5\\36y + 2y = 15\\[/tex]
It is a linear equation!
Option D:
[tex](2b * b-7) +b = 0\\2b ^ 2-7 + b = 0\\2b ^ 2 + b-7 = 0[/tex]
It is a quadratic equation!
ANswer:
Option D