Question 199338
There  are  actually  two  parabolas  that  meet  this  criteria,  a "y"  parabola,  and  an  "x"  parabola
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the  standard  form  for  a  "y"  parabola  is ,,,, ( y-k) = a (x-h)^2,  where (h,k)  is  the  vertex
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substituting  our  data,,,, vertex  at  (5, -7)  and  (4,1),,,,, ( y-(-7) ) = a (x-5)^2
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@ ( 4,1),,,,  (1) +7 =a ( 4-5)^2,,,,8=a(1),,,, a=8
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"y" parabola  is  y+7 = 8(x-5)^2,,,or  y= 8(x-5)^2 -7
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to  check  substitute  in both  given points,,,ok
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The  standard  form  for  an  "x"  parabola  is,,,,,(x-h) =a ( y-k)^2
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or (x-5) = a (y+7)^2,,,,,and  @ (4,1),,,,, (4-5) = a (1+7)^2,,,,a= -1/64
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or  (x-5) = -1/64 (y+7)^2,,,,,or  x= -1/64 (y+7) ^2 +5
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to  check  substitute  in  both  sets  of  points,,,,,,ok