What is the equation of the parabola that has a vertex at # (3, 1) # and passes through point # (23,6) #?

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What is the equation of the parabola that has a vertex at # (3, 1) # and passes through point # (23,6) #?

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Answer 1 · 2016-01-11T08:33:56

#80y = x^2 -6x +89#

Explanation:

The general vertex form of a parabola is #y=a(x-b)^2 + c#
where #(b,c)# is the vertex.
In this case this gives #b=3# and #c=1#
Use the values of the other point given to find #a#
#6 = a(23-3)^2 +1#
#6 = 400a+1#
#a=5/400 = 1/80#
Therefore #y=(x-3)^2/80 + 1#
#80y = (x-3)^2 + 80#
#80y = x^2 -6x +89#

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What is the equation of the parabola that has a vertex at # (3, 1) # and passes through point # (23,6) #?

1 Answer

Explanation:

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