Question 204874
x^2 -10x =2y-19
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complete  square,,,(10/2)^2 =25
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x^2 -10x +25 = 2y -19 +25,,,,,,,add  25  to  both  sides
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(x-5)^2 = 2y +6 = 2(y+3)
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(1/2) (x-5)^2 = (y+3),,,,form  is  A(x-h)^2 = (y-k)
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vertex  is  at  (h,k)  ,,,,or,,,(5,-3) 
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curve  is  an y  parabola,,,opening  up
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focus  is  at  (o,p)  where  p is  found  from  x^2 =4p y
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(x^2) = 2(y),,,,,or  4p = 2,,,p=1/2
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That  is  focus  is  1/2 above  center,,,or,,,(5, -2.5)
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x  intercepts  are  at  y=0,,,,,1/2(x-5)^2 =(0+3),,,(x-5)^2 =6,,(x-5)=sqrt6,
(x-5) = +/- 2.449,,,,x= 2.449,,,7.449
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directrix  is  at  (p) below  vertex,,,or  (y= -3.5)
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