Question

find the vertex,focus and directrix and the correct graph of the equation 8(x+3)=(y+2)^2

Answer 1

http://www.wolframalpha.com/input/?i=8%28x%2B3%29%3D%28y%2B2%29%5E2

Answer 2

rewrite the equation 8(x + 3) = (y+2)^2 general form for a parabola about the y-axis is

4a( x -h) = (y-k)^2 (h, k) is the vertex, x = -a is the equation of the directrix and (h+a, k) is the focus..

vertex is (-3, -2) a = 2 so the equation of the directrix is x = -2.... I'll let you figure the focus... just for something to do

Answer 3

solve for x

x = (1/8)(y+2)^2 - 3

vertex: (-3, -2)

directrix: x = -3 -1/(4a)
a = 1/8 --> x = -3 -2 = -5

Focus: (-3 +2, -2) = (-1,-2)