Answer
$$y = {x^2} - 4x - 2$$
Work Step by Step
$$\eqalign{
& \frac{{dy}}{{dx}} = 2x - 4 \cr
& {\text{Separate the variables}} \cr
& dy = \left( {2x - 4} \right)dx \cr
& {\text{Integrate both sides}} \cr
& \int {dy} = \int {\left( {2x - 4} \right)} dx \cr
& y = {x^2} - 4x + C{\text{ }}\left( {\bf{1}} \right) \cr
& {\text{Use the initial condition }}\left( {4, - 2} \right) \cr
& - 2 = {\left( 4 \right)^2} - 4\left( 4 \right) + C \cr
& - 2 = 16 - 16 + C \cr
& C = - 2 \cr
& {\text{Substitute }}C{\text{ into }}\left( {\bf{1}} \right) \cr
& y = {x^2} - 4x - 2 \cr
& \cr
& {\text{Graph}} \cr} $$
