SOLUTION: What is the vertex, axis of symmetry, focus, and directrix of the parabola y^2=-8x

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Question 408680: What is the vertex, axis of symmetry, focus, and directrix of the parabola y^2=-8x
Answer by MathLover1(20849) About Me  (Show Source):
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What is the vertex, axis of symmetry, focus, and directrix of the parabola y%5E2=-8x
since your parabola y%5E2=-8x is y^2 = 4px in standard form, that is a parabola with vertex at origin
The vertex is (0 ,0)
Directrix is x+=+-p
-8x%2Fx=4px%2Fx
-8=4p
-8%2F4=p
-2=p
Focus is at (p, 0)..........(-2, 0)
Since the x+axis+is the axis of symmetry of the parabola and its vertex is at the origin, the equation of the parabola has the form
y%5E2+=+4ax

The point (-2 , 4) lies on the parabola: 4%5E2+=4a%28-2%29
Solve for a: a = -2 ; the equation is: y%5E2+=+-8x




+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2Csqrt%28-8x%29%2C+-sqrt%28-8x%29%29+