What is the equation of the parabola that has a vertex at # (3, 3) # and passes through point # (13, 6) #?

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Answer 1 · 2017-08-03T05:15:55

The equation is #y=3/100(x-3)^2+3#

The equation of the parabola is

#y=a(x-h)^2+k#

Where #(h,k)# is the vertex

Therefore,

#h=3# and #k=3#

So, the equation is

#y=a(x-3)^2+3#

The parabola pases through the point #(13,6)#

so,

#6=a(13-3)^2+3#

#100a=3#

#a=3/100#

The equation is

#y=3/100(x-3)^2+3#

graph{y=3/100(x-3)^2+3 [-36.52, 36.54, -18.27, 18.28]}