[math]f_k\left(x\right)=x^2-2kx+k^2+\frac{1}{2}k+1[/math]
[math]f_k\left(x\right)=-\frac{1}{2k}x^2-x+2[/math]
[math]f_k\left(x\right)=x^2-2kx+2[/math]
[math]f_k\left(x\right)=\frac{1}{4}x^2-\frac{1}{2}kx-\frac{3}{4}k^2[/math]
[math]f_k\left(x\right)=-\frac{1}{2}x^2+4kx-10k^2+1[/math]