Answer
$$y = {x^2} - 6$$
Work Step by Step
$$\eqalign{
& \left( {\text{b}} \right) \cr
& \frac{{dy}}{{dx}} = 2x,{\text{ }}\left( { - 2, - 2} \right) \cr
& {\text{Separate the variables}} \cr
& dy = 2xdx \cr
& {\text{Integrate}} \cr
& \int {dy} = \int {2x} dx \cr
& y = {x^2} + C{\text{ }}\left( {\bf{1}} \right) \cr
& {\text{Use the initial condition }}\left( { - 2, - 2} \right){\text{ to find the particular solution}} \cr
& \left( { - 2} \right) = {\left( { - 2} \right)^2} + C \cr
& C = - 6 \cr
& {\text{Substituting }}C{\text{ into }}\left( {\bf{1}} \right) \cr
& y = {x^2} - 6 \cr
& \cr
& \left( {\text{a}} \right){\text{Slope field for the differential equation}} \cr
& \left( {\text{c}} \right){\text{Graph the solution}} \cr} $$
