Question 320392
Your derivation is correct except you made a small mistake by not distributing correctly,
{{{y(x)= -2(x^2-2xk +k)+4}}}
{{{y(x)= -2x^2 +4xk-2k +4}}}
{{{y(x)=-2x^2+4kx+(4-2k)}}}
Comparing to the general equation 
{{{y(x)=ax^2+bx+c}}}
{{{a=-2}}}
{{{b=4k}}}
{{{c=4-2k}}}
Since {{{k}}} is a constant, {{{4-2k}}} is also just a constant.