Describe how to graph the solution ofy ≤ −x2 + 2x.

Answer:We are given a inequality as:[tex]y\leq -x^2+2x[/tex]We know that the graph of this inequality will be a solid parabola ( since the inequality is with equality sign) .The parabola will be downward parabola ( Since for any general equation of parabola as y=ax^2+bx+c if a<0 then the parabola is downward and if a>0 then the parabola is upward)Also the roots of the parabola are the points where y=0.         (    The roots are:  -x(x-2)=0           x=0 and x=2 are the roots of the parabola)Also the region inside the parabola is shaded.         (This could be checked by taking different points)