# What are the vertex, focus, and directrix of the parabola described by #(x − 5)^2 = −4(y + 2)#?

##### 1 Answer

Aug 7, 2018

#### Explanation:

#"the standard form of a vertically opening parabola is"#

#•color(white)(x)(x-h)^2=4a(y-k)#

#"where "(h,k)" are the coordinates of the vertex and a"#

#"is the distance from the vertex to the focus and"#

#"directrix"#

#(x-5)^2=-4(y+2)" is in this form"#

#"with vertex "=(5,-2)#

#" and "4a=-4rArra=-1#

#"Focus "=(h,a+k)=(5,-1-2)=(5,-3)#

#"directrix is "y=-a+k=1-2=-1#

graph{(x-5)^2=-4(y+2) [-10, 10, -5, 5]}