Find the vertex focus and directrix of the following parabol

Find the vertex, focus, and directrix of the following parabola. Graph the equation. x^2 -4x = - y-2 The vertex is. (Type an ordered pair.) The focus is. (Type ordered pair.) The equation of the directrix is. (Type an equation.) Use the graphing tool to graph the equation.

Solution

x²-4x=-y-2

x²-4x +4=-y-2+4 =-y +2

(x-2)²-2=-y

y=-(x-2)²+2

center = (2,2)

focus (h,k +(1/4a) ) = (2,2 -1/4) = (2,7/4)

directrix

y=k -1/4a = 2+1/4 =9/4