Question 1083696

{{{x^2 + (y - 2)^2 = 4}}}

This is the equation of a circle. So we are looking to find an expression for the function that is the top half of the circle.

Functions are usually written in the form:
y = something; so, solve given equation for {{{y}}} 

{{{x^2 + (y - 2)^2 = 4}}}.....add {{{-x^2}}} to both sides

{{{x^2 -x^2+ (y - 2)^2 = -x^2+4}}}

{{{(y - 2)^2 = -x^2+4}}}.....take sqrt of both sides

{{{sqrt((y - 2)^2) = sqrt(-x^2+4)}}}

{{{y - 2 = sqrt(-x^2+4)}}}

{{{y = sqrt(-x^2+4)+2}}}

so, the top half of the circle is {{{ sqrt(-x^2+4)+2}}}

and the bottom  half of the circle is {{{ -sqrt(-x^2+4)+2}}}


here is a graph of the top half of the circle


{{{ graph( 600, 600, -10, 10, -10, 10, sqrt(-x^2+4)+2) }}}


here is a graph of the bottom half of the circle


{{{ graph( 600, 600, -10, 10, -10, 10, -sqrt(-x^2+4)+2) }}}


here is a graph of the whole circle


{{{ graph( 600, 600, -10, 10, -10, 10, sqrt(-x^2+4)+2,- sqrt(-x^2+4)+2) }}}