Answer:Option A[tex]y>x^{2} -4[/tex][tex]y<x^{2} +6[/tex]Step-by-step explanation:we know that1) The equation of the vertical parabola with y-intercept -4 is equal to[tex]y=x^{2} -4[/tex]The solution of the inequality is the shaded area above the dashed linesoThe inequality must be[tex]y>x^{2} -4[/tex]2) The equation of the vertical parabola with y-intercept 6 is equal to[tex]y=x^{2}+6[/tex]The solution of the inequality is the shaded area below the dashed linesoThe inequality must be[tex]y<x^{2} +6[/tex]therefore The system of inequalities graphed is[tex]y>x^{2} -4[/tex][tex]y<x^{2} +6[/tex]