#"the equation of a horizontally opening parabola is"#
#•color(white)(x)(y-k)^2=4a(x-h)#
#"where "(h,k)" are the coordinates of the vertex and a is"#
#"the distance from the vertex to the focus and directrix"#
#"If "a>0" opens to the right "#
#"If "a<0" opens to the left"#
#"rearrange the given equation into this form"#
#(y-2)^2=-(x-3)#
#"with vertex "=(3,2)#
#4a=-1rArra=-1/4" so opens to the left"#
#"Focus "=(a+h,k)=(-1/4+3,2)=(11/4,2)#
#"directrix is "x=-a+h=1/4+3=13/4#
#"for x-intercept let y = 0"#
#4=-x+3rArrx=-1#
#"for y-intercepts let x = 0"#
#(y-2)^2=3rArr(y-2)=+-sqrt3#
#y=2+-sqrt3#
#y~~3.73,y~~0.27#
#"Plot the above coordinates for vertex, focus and "#
#"intercepts and draw a smooth curve through them"#
graph{(y-2)^2=-(x-3) [-10, 10, -5, 5]}
