Question 1089163: convert the equation to standard for by completing the square on x. Then find the vertex, focus and directrix of the parabola. then graph
x^2+2x-8y-31=0
Answer by MathLover1(20850)   (Show Source):
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The "vertex" form of a parabola with its vertex at ( , ) is:
regular: 
sideways: 
The conics form of the parabola equation (the one you'll find in advanced or older texts) is:
regular: 
sideways: 
where the value of  is actually the same as the value of 
 ....since coefficients  and  , we have  -> ->
 =>  and  , and
the vertex is at ( , )
The focus is "p" units from the vertex:
 ,
so 
then,
the focus is  unit above the vertex, at (,  ),
and the directrix is the horizontal line , p or   below the vertex
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