Question 1051947
Work through the algebraic steps to find  {{{x^2+(y-1)^2>=9}}} and make a sketch of this circle centered at (0,1) with radius of 3.  BETWEEN the x-intercepts, y values will be positive or 0.


What are the x-intercepts, where y=0?
{{{y=0=sqrt(9-x^2)+1}}}
{{{-1=sqrt(9-x^2)}}}
{{{x^2-9=-1}}}
{{{x^2=8}}}
{{{x=0+- 2*sqrt(2)}}}
Some steps here were omitted.


Between inclusive, {{{-2sqrt(2)}}} and {{{2sqrt(2)}}}, y will be positive or 0.  You would shade the region ABOVE the circle for x values between and including those two values.



<b>Note that neither of these graphs look the way they need to be.  You want to shade ONLY the region between the x-intercepts ABOVE AND INCLUDING the circle.</b>  (My use of the site's code is just not right, or I do not yet know this code well enough.)


{{{graph(300,300,-5,5,-5,5,x^2+(y-1)^2>=9)}}}


{{{graph(300,300,-5,5,-5,5,y-1>=sqrt(9-x^2))}}}