Question 609826: find the vertex, value of p, axis of symmetry, focus, and directrix y-2+-1/8(x+2)^2
Answer by ewatrrr(24785)   (Show Source):
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Hi
Note: the vertex form of a parabola opening up or down,  where(h,k) is the vertex.
y-2+-1/8(x+2)^2 ||Assuming you meant: y - 2 = (-1/8)(x+2)^2
y = (-1/8)(x+2)^2 + 2 ||Vertex(-2,2), axis of symmetry is x = -2
The standard form is  , where the focus is (h,k + p)
(x+2)^2 = -8(y-2)^2 , 4p = -8,  and focus is (-2,0), directrix is y= 4
See below descriptions of various conics
Standard Form of an Equation of a Circle is 
where Pt(h,k) is the center and r is the radius
Standard Form of an Equation of an Ellipse is  where Pt(h,k) is the center. (a positioned to correspond with major axis)
a and b are the respective vertices distances from center and ± are the foci distances from center: a > b
Standard Form of an Equation of an Hyperbola opening right and left is:
 where Pt(h,k) is a center with vertices 'a' units right and left of center.
Standard Form of an Equation of an Hyperbola opening up and down is:
 where Pt(h,k) is a center with vertices 'b' units up and down from center.
the vertex form of a parabola opening up or down, where(h,k) is the vertex.
The standard form is , where the focus is (h,k + p)
the vertex form of a parabola opening right or left,  where(h,k) is the vertex.
The standard form is  , where the focus is (h +p,k )
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