#"the equation of a parabola in "color(blue)"vertex form"# is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))#
#"where "(h,k)" are the coordinates of the vertex and a"#
#"is a multiplier"#
#"to obtain this form use the method of "color(blue)"completing the square"#
#• " coefficient of "x^2" term must be 1 which it is"#
#• " add/subtract "(1/2"coefficient of x-term")^2" to "x^2-4x#
#y=x^2+(-2)xcolor(red)(+4)color(red)(-4)+5#
#rArry=(x-2)^2+1larrcolor(blue)"in vertex form"#
#rArr"vertex "=" centre of circle "=(2,1)#
#x=0toy==5larrcolor(blue)"y-intercept"#
#"the radius of the circle is the distance from the"#
#"centre to the point "(0,5)#
#"to calculate radius use the "color(blue)"distance formula"#
#•color(white)(x)r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#
#"let "(x_1,y_1)=(2,1)" and "(x_2,y_2)=(0,5)#
#r=sqrt((0-2)^2+(5-1)^2)=sqrt20=2sqrt5#
#"the equation of a circle in standard form is "#
#color(red)(bar(ul(|color(white)(2/2)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(2/2)|)))#
#"where "(a,b)" are the coordinates of the centre and "#
#"r is the radius"#
#rArr(x-2)^2+(y-1)^2=20larrcolor(blue)"equation of circle"#
graph{(y-x^2+4x-5)((x-2)^2+(y-1)^2-20)((x-2)^2+(y-1)^2-0.05)=0 [-10, 10, -5, 5]}
