SOLUTION: vertex: ? focus point: ? equation of the axis of symmetry: ? equation of directrix: ? 2 random points on equation: ? y^2 + 8x + 8 = 0

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Question 980451: vertex: ?
focus point: ?
equation of the axis of symmetry: ?
equation of directrix: ?
2 random points on equation: ?
y^2 + 8x + 8 = 0

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Best thing is use the derived equation for parabola translated from standard position, y%5E2=4px becomes %28y-k%29%5E2=4p%28x-h%29 for which the vertex is (h,k). The distance from vertex to either focus or directrix is absolute value of p.

8x%2B8=-y%5E2
8%28x%2B1%29=-y%5E2
-8%28x%2B1%29=y%5E2

This is concave to the left and has vertex (-1,0).
Axis of symmetry is y=0.

-8=4p
p=-2
Meaning the focus and directrix are both two units away from the point (-1,0). Focus must be on the concave side, so (-3,0) is the focus, and (1,0) is a point on the directrix. Directrix is x=1.