Which quadratic equation fits the data in the table?

Answer: [tex]y=x^2-4x+1[/tex]First option is correct.Step-by-step explanation:From the given table, we take three points (0,1), (1,-2) and (2,-3)Now, let the  quadratic equation is [tex]y=ax^2+bx+c[/tex]Use the first point (0,1) [tex]1=a(0)^2+b(0)+c\\\\c=1[/tex]Thus, the equation becomes [tex]y=ax^2+bx+1[/tex]Now, use the point (1,-2) [tex]-2=a(1)^2+b(1)+1\\\\a+b+1=-2\\\\a+b=-3...(i)[/tex]Now, use the point (2,-3) [tex]-3=a(2)^2+b(2)+1\\\\4a+2b+1=-3\\\\4a+2b=-4\\\\2a+b=-2...(ii)[/tex]Subtract (i) and (ii)a-2a= -3+2-a = -1a = 1Now, substituting this value in (i)1 + b = -3b = -3-1b = -4Therefore, the quadratic equation is [tex]y=x^2-4x+1[/tex]First option is correct.