SOLUTION: Find the vertex, focus, directrix, and focal width of the parabola. -2x^2+20x-y-52=0

Question 893609: Find the vertex, focus, directrix, and focal width of the parabola. -2x^2+20x-y-52=0
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the vertex, focus, directrix, and focal width of the parabola.
-2x^2+20x-y-52=0
complete the square:
-2(x^2-10x+25)=y+52-50
-2(x-5)^2=y+2
(x-5)^2=-(1/2)(y+2)
This is an equation of a parabola that opens downward.
Ita basic form of equation: (x-h)^2=-4p(y-k)
For given parabola:
4p=1/2
p=1/8
vertex:(5,-2)
axis of symmetry: x=5
focus:(5,-17/8)(p-distance below vertex on the axis of symmetry)
directrix:-15/8 (p-distance above vertex on the axis of symmetry)
focal width=4p=1/2

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