What is the equation of the parabola that has a vertex at # (77, 7) # and passes through point # (82,32) #?

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Answer 1 · 2017-07-26T17:08:49

#y=(x-77)^2+7#

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

Since the vertex is at #(77,7)#, #h=77# and #k=7#. We can rewrite the equation as:

#y=a(x-77)^2+7#

However, we still need to find #a#. To do this, substitute the given point #(82, 32)# in for the #x#- and #y#-values.

#32=a(82-77)^2+7#

Now, solve for #a#.

#32=a(82-77)^2+7#
#32=a(5)^2+7#
#32=25a+7#
#25=25a#
#a=1#

The final equation is #y=1(x-77)^2+7#, or #y=(x-77)^2+7#.