What is the equation of the parabola that has a vertex at # (1, 4) # and passes through point # (3,-9) #?

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Answer 1 · 2018-04-28T11:22:53

# (y-4)=-13/4(x-1)^2, or, 13x^2-26x+4y-3=0#,

We know that, # S : (y-k)=a(x-h)^2#, represents a parabola

with the vertex #(h,k)#.

So, let # S : (y-4)=a(x-1)^2#, be the reqd. parabola.

Given that #(3,-9) in S#, we have,

# (-9-4)=a(3-1)^2#.

#:. a=-13/4#.

# :. S : (y-4)=-13/4(x-1)^2, or, #

# S : 13x^2-26x+4y-3=0#,