What is the standard equation of parabola whose vertex is #(3,2)# and passes through #(-1,14)#?

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Answer 1 · 2016-05-27T12:53:56

#3x^2-18x-4y+35=0#

Standard form of parabola is #y=a(x-h)^2+k# where #(h,k)# is the vertex. As vertex is #(3,2)#, this is

#y=a(x-3)^2+2# and as it passes through #(-1,14)#

i.e. #14=a(-1-3)^2+2#

or #14=a(-4)^2+2#

or #14=16a+2#

or #16a=12# and hence #a=12/16=3/4#

Hence equation of parabola is

#y=3/4(x-3)^2+2#

or #4y=3(x^2-6x+9)+8#

or #3x^2-18x-4y+35=0#